# SSC CGL Tier 1 and Tier 2 Program

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1 Gurudwara Road Model Town, Hisar SSC CGL Tier 1 and Tier 2 Program Section : Math Chapter : Geometry Days Geometry Significance: 7-8 questions can come in tier 1 and questions in tier 2. This chapter will come under advance math What is advance math? Many people consider these four (geometry, algebra, Mensuration, trigonometry) chapters difficult, many people consider high weightage in overall math. According to me nothing is advance just concentration and practice make you scoring these four topics. So I will call it as scoring math. Atleast 4-5 questions will be directly related to properties. So understanding properties will be highly useful. Remember properties and should be on your tips. What will we cover in Geometry chapter? Lines Angles Triangle Quadrilateral Polygons Circles Let us start from lines Parallel lines: those two or more lines which will never meet just like railway track lines. Transverse line: A line which will cut parallel lines. It is shown diagrammatically below. From a point N number of lines can be drawn. As many as you wish. Understand angles making with lines. AB and CD are parallel lines. Symbol of parallel lines is. You will find many places symbol of line like or simply AB; both are same thing. EF: - Transversal lines Corresponding Angles Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 1

2 1 = 5 Alternate angles 1 = 7 or 4 = 6 or 3 = 5 etc E 1 2 A B C D 8 7 F Adjacent angles = in this case as these are linear pair. Any two angles which are adjacent are called adjacent angles. It is not necessary that their sum should be. Sum of interior Angles same side = 2 right angle = = 180 Sum of Exterior Angles same side 1 = 8 = 180 Vertically opposite angles = 1 = 3 or 2 = 4 Internal Angle Bisector = angle divided in two equal parts Internal Q Q Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 2

3 External Angle bisector Q Q Angle = 8 Types 1. Acute An gle = Right Angle = Obtuse Angle = Straight Angle = Reflex Angle = Complete Angle = Complementary Angle = Sum of 2 Angles = Supplementary Angle l= Sum of two Angle = TRIANGLE What is vertex (singular, vertices (plural) : Vertices A, B, C shown in diagram How to show angles: Angle = A, B, C How to show sides: Three sides = AB, BC, AC Triangle can be classified in two ways: based on sides and based on angles Triangles are of 3 Types based on sides Equilateral Triangle = all three sides equal Isosceles Triangle = any two sides equal Scalene = all three sides are different in length Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 3

4 Triangles are of 3 Types based on angles also Right angle triangle : one angle will be of 90 degree Obtuse angle : one angle will be more than 90 degree Acute Angle : all three angles should be less than 90 degree Congruency of Triangle ( congruent triangles are those that have similar size and shape ; this means corresponding sides are equal and corresponding angles are equal) Rules that help to decide congruency: Two triangles will be congruent if : SSS: (Side- Side Side rule): When all three sides are equal SAS: (Side Angle Side Rule): When two sides and one angle are equal Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 4

5 ASA: (Angle Side Angle Rule): When two angles and one side are equal Hypotenuse Leg Rule / Right Angle- Hypotenuse- Side ( RHS) rule Similarity of triangles A P B C Q R A ; Perimeter of = P Q B C Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 5

6 PQ BC ; P and Q are mid points of AB and AC respectively. PQ = In case of Angle bisector P Q S R PS is common side ; If DE intersect lines AB and AC at D and E then A D E 5 B 9 C e.g. AD =2.5 ; DB =5 ; AE =2; BC = 9 ; then what will be DE and EC. Value of EC will be 4 and value of DE will be =3 Altitude You can call it height also Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 6

7 Orthocenter A F e O B D C All three Altitudes meet at O Angle Bisector I = incentre Circle inscribed in the triangle A F i E B D C ID = IE = IF ( will be radius) BIC = 90 + for Internal Angle Bisector A B C P Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 7

8 Bisector External Angle BPC = Perpendicular bisector Mid points of side Perpendicular to it Circle circumscribed about the triangle P F E G Q D R PG = RG = QG QGR = 2 P also these will be radium of the circle always angle formed at centre is double of angle formed at circumference Median Median : the line drawn from vertex to mid- point of opposite side Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 8

9 Each median is divided into 1 : 2 at centroid. ; Point of concurrency is called: Meeting Point ; G = Centroid Apollonius theorem : It is related to Median A F G E B D C AB 2 + AC 2 = 2 (AD 2 + BD 2 ) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 9

10 Other key points for median A 3 D F E G B M C Ratio of AF : FG is always in 3: Area of If area of Other facts about triangle C A B Sum of two sides is always greater than third side : e.g. AB + BC > CA ; AB + AC > BC ; BC + CA > AB Difference of two sides is always lesser than third side : AB BC < CA ; AB AC < BC ; BC CA < AB Quadrilateral Parallelogram: Opposite sides equal and parallel D C O A B Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 10

11 AB = DC, AD = BC A + B = B + C = C + D = D + A = A = C and B = D AC, AO = OC, OB = OD Rhombus All sides are equal, parallel D C O A B A + B = B + C = C + D = D + A = A = C, B = D 4 = Sum of square of sides = Sum of square of diagonals Diagonals bisect Each other at right angle Form four right angled triangles Diagonals : Not of equal magnitudes Four right triangles Each equal th of area of rhombus. Rectangle D C O A B Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 11

12 Square AB = CD AD = BC A = B = C = D = 90 0 Diagonals are equal Bisect each other AC = BD OA = OB = OC = OD Diagonals bisect each other at right angle Triangle 4 isosceles right angle Triangles AB = BC = CD = AD A = B = C = D 0 Diagonals of square AC = BD Trapezium AB DC D C A B Only one pair of opposite sides are parallel Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 12

13 Cyclic quadrilateral 2 A 2 D C Polygons Convex polygon:- none of its interior angle more than Concave polygon: At least one angle is more than Regular polygon = Sides & Angles equal Exterior Angle = ; Interior Angle = _ Exterior Angle In case of convex polygon, sum of all interior angles = (2n 4) Exterior Angles sum = 36 No of diagonal = CIRCLE Angles in same segment are equal Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 13

14 Angle in semi circle: Right Angle Two chords intersect each other internally Or Externally AE A O E D C B Internally A B O E D C Externally Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 14

15 Tangents to a Circle (i) O P T T = Point of contact OT PT (ii) A P O B PA = PB ; P = outside point From any outside point P, distance of both tangents is equal. (iii) A B Q Q P T Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 15

16 Angle made by chord with tangent is always equal to the angle on any point of circumference. PTA = ABT AT = Chord PT Tangent to circle (iv) Below is the important properties, frequently asked in SSC /competitive exams. A B D C AB. AC + DE. AE = AE 2 E (v) A B D P C PA Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 16

17 (vi) T P A B PT 2 = PB P = External Point T = Point of Contact PAB = secant to the circle PT = Tangent PAIR OF CIRCLES (I) A C B A, B,C Collinear C Point of Contact of the two circles Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 17

18 (ii) A E O d B F H D L C G Direct Tangents: Length of the direct common tangent (L) = ; d = distance between two centers, r and (iii) O d d Length of transverse Tangent (L) = (iv). When two circles touch then d = r 1 + r 2 Cyclic Quadrilateral A + C = B + D = Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 18

19 Sum of opposite Angles = A B D C Project 400 Questions Q 1.ABCD is a rhombus in which side AB = 4 cm and ABC = 120 0, then the length of the diagonal BD is (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm Solution : (d) ABC = ; ABD = 6 0 ; ABD = ADB = 60 0 ; AB = AD ; ABD is an equilateral ; BD = 4 cm Q 2. If I be the incentre of ABC and B = 70 and C = 50, then the magnitude of BIC is (a) 130 (b) 60 (c) 120 (d) 105 Solution :(c) IBC 35 ICB Q 3. In ABC, D is the mid- point of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of ABC is equal to (a) 3 cm (b) 6 cm (c) 9 cm (d) 15 cm Solution :(a) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 19

20 AD = 27 cm; Centroid = O; ; = 2 ; ND = 12 cm; 2 3 Q 4. A tree of hight h metres is broken by a storm in such a way that its top touches the ground at a distance of x metres from its root. Find the height at which the tree is broken. (Here h>x (d) 20 ) Solution :(b) (a) metre (b) metre (c) metre (d) metre AB = Height of tree = h metre ; AC = Required height = y metre; BC = CD = Broken part of tree =(h y) metre AC 2 + AD 2 = CD 2 y 2 + x 2 = (h y) 2 y 2 + x 2 = h 2 + y 2 2hy x 2 = h 2 2hy 2hy h 2 x 2 y Q 5. For a triangle ABC, D, E, F are the mid-points of its sides. If ABC = 24 sq. units then DEF is (a) 4 sq. units (b) 6 sq. units (c) 8 sq. units (d) 12 sq. units Solution :(b) Q 6. The in-radius of an equilateral triangle is of length 3 cm. The length of each of its medians is (a) 12 cm (b) cm (c) 4 cm (d) 9 cm Solution :(d) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 20

21 In equilateral triangle centroid, incentre, orthocentre coincide at the same point. ; ; 3 3 Q 7. The radius of two concentric circles are 17 cm and 10 cm. A straight line ABCD intersects the larger circle at the point A and D and intersects the smaller circle at the points B and C. If BC = 12 cm, then the length of AD (in cm) is: (a) 20 (b) 24 (c) 30 (d) 34 Solution :(a) BE = EC = 6 cm, OB = 10 cm, OA = 17 cm; From ; OE = ; From ; AE = 25 5 ; Q 8. The radius of the circum circle of a right angled triangle is 15 cm and the radius of its inscribed circle is 6 cm. Find the sides of the triangle. (a) 30, 40, 41 (b) 18, 24, 30 (c) 30, 24, 25 (d) 24, 36, 20 Solution :(b) Simply, check through options & find Pythagorean Triplet = 30 2 ; 24 3 Q 9. Two circles are of radii 7 cm and 2 cm their centres being 13cm apart. Then the length of direct common tangent to the circles between the points of contact is (a) 12 cm (b) 15 cm (c) 10 cm (d) 5 cm Solution :(a) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 21

22 Direct common tangent; ; = Q 10. If the radii of two circles be 6 cm and 3 cm and the length of the transverse common tangent be 8 cm, then the distance between the two centres is (a) (b) (c) (d) Solution :(a) Length of transverse tangent;= 64 XY 2 81 XY XY 45 Q 11. Two parallel chords are drawn in a circle of diameter 30 cm. The length of one chord is 24 cm and the distance between the two chords is 21 cm. The length of the other chord is (a) 10 cm (b) 18 cm (c) 12 cm (d) 16 cm Solution :(b) AB 24 cm AE EB 2 cm OE ; Also, CF = 2 Q 12. Two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. The length of the common chord is: (a) 2 cm (b) 4 cm (c) 2 cm (d) 8 cm Solution :(b) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 22

23 OC = 2 cm; OA = 4 cm; ; 4 3 Q 13. Two circles touch each other internally. If their radii are 2 cm & 3 cm. Find the length of that chord of larger circle which touches the smaller one. (a) 2 cm (b) 4 cm (c) 3 cm (d) None of these Solution :(b) PQ = 3 cm, OP = 2 cm OQ = (3 2 cm cm OC OQ QC 2 QC OC cm AQ 3 cm AC = ; AB = 2AC = Q 14. ABCD is a trapezium whose side parallel to. Diagonal and intersect at O. If = 3, = x 3, = 3x 19 and = x 5, the value (s) of x will be: (a) 7, 6 (b) 12, 6 (c) 7, 10 (d) 8, 9 Solution :(d) Clearly, ; 5 x 2 x 5 x 2 x 2 x 2 8x 9x 2 x x 8)-9(x x 8)(x x or Q 15. The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the centroid of the ADC respectively the length of the line segment PQ is (a) 4 cm (b) 6 cm (c) 9 cm (d) 12 cm Solution :(b) ABC and Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 23

24 Centroid is the point where medians intersect. Diagonals of parallelogram bisect each other. OP = 3 ; OQ = 3 ; 6 Q 16. The sum of the interior angles of a polygon is The number of sides of the polygon is (a) 6 (b) 9 (c) 10 (d) 12 Solution :(c) Sum of interior angles of regular polygon = (2n 4) Q 17. An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is (a) 14 (b) 16 (c) 12 (d) 18 Solution :(c) If the number of sides of regular polygon be n, then each interior angle = 2 2 ; And each exterior angle = ; n 2 Q 18. Ratio of the number of sides of two regular polygons is 5 : 6 and the ratio of their each interior angle is 24 : 25. Then the number of sides of these two polygons is (a) 20, 24 (b) 15, 18 (c) 10, 12 (d) 5, 6 Solution :(c) Let the number of sides be 5x and 6x respectively. ; Then, ; [ ] 25x 10 = 24x x 8 = 2; 2 Q 19. ABCD and ADEF are parallelograms in the given figure. If CA = AF and ACD = 60 0 then DECF =? (a) 30 0 (b) 60 0 (c) 75 0 (d) 80 0 Solution :(a) AC = AF ACF = AFC = x(suppose) ; ACD = 60 0 FCD = (60 0 x) BF CE AFC = ECF ; x = 60 0 x 2x = 60 0 x = x = Q 20. The length of the sides forming the right angle in a right angled triangle is a and b. Three squares are inscribed outwards on the three sides of the triangle. What is the total sum of the area of the triangles and that of the squares so formed? (a) 2(a 2 + b 2 ) + ab (b) 2(a 2 + b 2 ) ab (c) 2(a 2 + b 2 ) ab (D) 2.5(a 2 + b 2 ) Solution :(c) AB = a BC = b ; AC = Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 24

25 Area of ; Area of square on sides AB = a 2 Area of square on side BC = b 2 Area of square on side AC = Total required area = a 2 + b 2 + b 2 + a 2 = 2(a 2 + b 2 ) ab Q 21. In ABC, A = 90 and AD BC where D lies on BC. If BC = 8 cm, AC = 6 cm, then ABC : ACD =? (a) 4 : 3 (b) 25 : 16 (c) 16 : 9 (d) 25 : 9 Solution :(c) In Ratio of area of triangles = ratio of square of their corresponding sides Hence, 6 Q 22. For a triangle, base is 6 cm and two base angle are 30 and 60. Then height of the triangle is (a) 3 cm (b) 4.5 cm (c) 4 cm (d) 2 cm Solution :(b) Sin ; Also, sin 60 AD 4 5 Q 23. ABC is a right-angled triangle with AB = 6cm and BC = 8 cm. A circle with centre O has been inscribed inside ABC. The radius of the circle is (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm Solution :(b) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 25

26 AC = ; OD = OE = OF = radii = r cm; Area of [ = 6 6; 3r + 4r + 5r = 24 12r = 24 r = 2 Q 24. If the radius of the circum circle of an equilateral triangle is 10 cm, then what will be the radius of the incircle inscribed in it? (a) 5 cm (b) 10 cm (c) 20 cm (d) 15 cm Solution :(c) Ar (ABE) = ; OB : OE = 2 : 1 Ar (DOE) = ; (a) Since the ratio of the radius of incircle and circumcircle of an equilateral 2 Q 25. In the given figure ABC = (a) 3 cm (b) 4 cm (c) 5 cm (d) 6 cm Solution :(c) AC = 6 So, AM = MC = 5 cm. The midpoint of the diagonal AC is equidistant from the vertices A, B and C BM = AM = MC = 5 cm. Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 26

27 Q 26. A parallelogram ABCD and a rectangle ABEF are drawn between parallel lines EF and CD. If AB = 7cm and BE = 6.5 cm, then area of parallelogram will be (a) 22.75cm 2 (b) cm 2 (c) 45.5 cm 2 (d) 45.0 cm 2 Solution :(c) Area of rectangle ABEF = Parallelogram ABCD and rectangle ABEF are based on the same base AB and between the same parallels AB CF) 45 5 cm 2 Q 27. The area of 2. XY is drawn parallel to BC which divides AB in the ratio 3 : 5. If BY is joined then area of (a) 3.5 cm 2 (b) 3.7 cm 2 (c) 3.75 cm 2 (d) 4.0 cm 2 Solution :(c) ; ; Ar(AXY) = 2 25 Q In the adjoining figure ABCD is a rectangle in which AE = EF = FB. Then the ratio of the areas of (a) 1 : 4 (b) 1 : 6 (c) 2 : 5 (d) 2 : 3 Solution :(b) Let BC x and FB y EF AE CD 3y Now ar ar 2 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 27

28 ; Area of rectangle ABCD = 3xy ( ) Q 29. In the adjoining figure the value of x is (a) 6 cm (b) 7 cm (c) 6.7 cm (d) 7.7 cm Solution :(c) PD ; (7 + x) 2 ; 7 + x = ; X = = 6.7 Q 30. In the given figure O is the centre of the circle. If AOC = then the value of ABC is (a) (b) (c) (d) Solution :(a) B = = Q 31. In the given figure O is the centre of the circle. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP > PB then value of AP is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 28

29 (A) 12 cm (b) 24 cm (c) 8 cm (d) 6 cm Solution :(a) AP 6 6 x 2 16x + 48 = Q 32. In the given figure O is the centre of the circle then value of x is (a) 60 0 (b) 45 0 (c) 15 0 (d) 30 0 Solution :(d) In OB = OC ; B = C = 30 0 ; [ ; D = 30 0 Q 33. In the given the value of x is (a) 2.2 cm (b) 1.6 cm (c) 3 cm (d) 2.6 cm Solution :(a) From the given figure, PT 2 = PA ; 6 2 = 5(5 + x) ; 5 + x = ; x = = 2.2 cm Q 34. AB is the diameter of the circle and O is its centre. CD and AB intersect in such a way that OE = EB and CE = 6 cm, ED = 2 cm. Find the radius of the circle. Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 29

30 (a) 4 cm (b) 6 cm (c) 4 cm (d) 8 cm Solution :(a) Let the radius of the circle be r 2. Now, AE ( ) Q 35. In the given figure A, B, C are points on the circumference of the circle and O is the centre. If ABC is (a) 60 0 (b) 75 0 (c) 90 0 (d) None of these Solution :(b) AOC = ( ) = Q 36. In the given figure AD : DC = 2 : 3 then ABC is (a) 30 (b) 40 (c) 45 (d) 110 Solution :(b) ; ; Q 37. In the given figure PQ is a tangent at point K, and LN is the diameter. If KLN = 30 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 30

31 (a) 30 0 (b) 50 0 (c) 60 0 (d) 70 0 Solution :(c) LKN = 90 0 (angle of the semicircle) ( ) = (angle in the alternate segment) Q 38. In the given figure XY AC, and XY divides the triangle into two equal parts. Then (a) (b) (c) Solution :(b) 2 (d) Q In the given figure AM BC and AN is the bisector of A. Then MAN will be- (If B = 65 0, C = 33 (a) 33 (b) 16 (c) 16 0 (d) 32 0 Solution :(c) MAN = Q 40. In the adjoining figure find the value of QSR Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 31

32 (a) 50 0 (b) 65 0 (c) 70 0 (d) 75 0 Solution :(b) PQO = PRO = 90 0 [radii are perpendicular on tangents at the points of contact] In Quadrilateral PQOR, ROQ = ( ) = = QSR = QOR = 3 65 [Angle subtended by an arc on the remaining part of the circle is half the angle subtended on the centre.] Practice Questions Geometry 500 Series Advance math 1. Point P is inside BAC, if BAC = & PAC = 70 0 then find BAP. (a) 70 0 (b) (c) 45 0 (d) None of these 2. If AOB = 75 0, BOC = then choose the correct answer: (a) OC AB (b) OC OA (c) O, C & A are collinear (d) None of these 3. If point I is the incentre of ABC and BIC = 135 0, then (a) Acute angle (b) Equilateral triangle (c) Right angle triangle (d) Obtuse angle triangle 4. ABCD is a rhombus in which side AB = 4 cm and ABC = 120 0, then the length of the diagonal BD is (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm 5. In a ABC, A + B = 118, A + C = 96. Find the value of A. (a) 36 (b) 40 (c) 30 (d) In a ABC, A = 3 B = 70 and B + C = 130, value of A is (a) 20 (b) 50 (c) 110 (d) In a triangle ABC, A + B + C = 140, then B is (a) 50 (b) 80 (c) 40 (d) If I be the incentre of ABC and B = 70 and C = 50, then the magnitude of BIC is (a) 130 (b) 60 (c) 120 (d) O is the in-centre of the ABC, if BOC = 116, then BAC is (a) 42 (b) 62 (c) 58 (d) In a triangle ABC, incentre is O and BOC = 110, then the measure of BAC is: (a) 20 (b) 40 (c) 55 (d) The circumcentre of a triangle ABC is O. If BAC = 85 and OAC =75 0, then the value of OAC is (a) 40 (b) 60 (c) 70 (d) In ABC, D is the mid- point of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of ABC is equal to (a) 3 cm (b) 6 cm (c) 9 cm (d) 15 cm Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 32

33 13. The side BC of a triangle ABC is extended to D. If ACD = 120 and ABC = CAB, then the value of ABC is (a) 80 (b) 40 (c) 60 (d) In a ABC, If 2 A = 3 B = 6 C, value of B is (a) 60 (b) 30 (c) 45 (d) A tree of hight h metres is broken by a storm in such a way that its top touches the ground at a distance of x metres from its root. Find the height at which the tree is broken. (Here h>x) (a) metre (b) metre (c) metre (d) metre 16. In a ABC, the medians AD, BE and CF meet at G, then which of the following is true? (a) AD + BE + CF > (AB + BC + AC) (b) 2(AD + BE + CF) > (AB + BC + AC) (c) 3(AD + BE + CF) > 4(AB + BC + AC) (d) 4(AD + BE + CF) >3(AB + BC + AC) 17. The internal bisectors of the angles B and C of a triangle ABC meet at I. If BIC = + X, then X is equal to (a) 60 (b) 30 (c) 90 (d) The measure of the angle between the internal and external bisectors of an angle is (a) 60 (b) 70 (c) 80 (d) AD is the median of a triangle ABC and O is the centroid such that AO = 10 cm. Length of OD (in cm) is (a) 2 (b) 4 (c) 5 (d) In a triangle ABC, median is AD and centroid is O. AO = 10 cm. The length of OD (in cm) is (a) 6 (b) 4 (c) 5 (d) If in a triangle ABC, D and E are on the sides AB and AC, such that, DE is parallel to BC and =. If AC = 4 cm, then AE is (a) 1.5 cm (b) 2.0 cm (c) 1.8 cm (d) 2.4 cm 22. O is the incentre of ABC and A = 30, then BOC is (a) 100 (b) 105 (c) 110 (d) The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the smallest angle is (a) 30 (b) 60 (c) 45 (d) If the angles of a triangle ABC are in the ratio 2 : 3 : 1, then the angles A, B and C are (a) A = 60 B = 90, C = 30 (b) A = 40 B = 120, C = 20 (c) A = 20 B = 60, C = 60 (d) A = 45 B = 90, C = In a ABC, D and E are two points on AB and AC respectively such that DE BC, DE bisects the ABC in two equal areas Then the ratio DB : AB is (a) 1 : 2 (b) 1 : 2 (c) ( 2-1) : 2 (d) 2 : In triangle ABC a straight line parallel to BC intersects AB and AC at D and E respectively. If AB = 2AD then DE : BC is (a) 2 : 3 (b) 2 : 1 (c) 1 : 2 (d) 1 : Two supplementary angles are in the ratio 2 : 3 The angles are (a) 33, 57 (b) 66, 114 (c) 72, 108 (d) 36, In ABC, If AD BC, then AB 2 + CD 2 is equal to (a) 2 BD 2 (b) BD 2 + AC 2 (c) 2 AC 2 (d) None of these 29. If in a triangle ABC as drawn in the figure, AB = AC and ACD = 120, then A is equal to (a) 50 (b) 60 (c) 70 (d) 80 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 33

36 (a) 31 (b) 33 (c) 35 (d) In the following figure, AB be diameter of a circle whose centre is O. If AOE = 150, DAO = 51 then the measure of CBE is: (a) 115 (b) 110 (c) 105 (d) In a ABC, AB = AC and BA is produced to D such that AC = AD. Then the BCD is (a) 100 (b) 60 (c) 80 (d) Two chords AB, CD of a circle with centre O intersect each other at P. ADP = 23 and APC = 70 then the BCD is (a) 45 (b) 47 (c) 57 (d) In triangle PQR, points A, B and C are taken on PQ, PR and QR respectively such that QC = AC and CR = CB. If QPR = 40 then ACB is equal to: (a) 140 (b) 40 (c) 70 (d) Internal bisectors of angles B and C of a triangle ABC meet at O. If BAC = 80, then the value of BOC is (a) 120 (b) 140 (d) 110 (d) In ABC, draw BE AC and CF AB and the perpendicular BE and CF intersect at the point O. If BAC = 70, then the value of BOC is (a) 125 (b) 55 (c) 150 (d) The angle between the external bisectors of two angles of a triangle is 60. Then the third angle of the triangle is (a) 40 (b) 50 (c) 60 (d) Internal bisectors of B and C of ABC intersect at O. If BOC = 102, then the value of BAC is (a) 12 (b) 24 (c) 48 (d) A circle (with centre at O) is touching two intersecting lines AX and BY. The two points of contact A and B subtend an angle of 65 at any point C on the circumference of the circle. If P is the point of intersection of the two lines, then the measure of APO is (a) 25 (b) 65 (c) 90 (d) The internal bisectors of ABC and ACB of ABC meet each other at O. If BOC = 110, then BAC is equal to (a) 40 (b) 55 (c) 90 (d) ABCD is a quadrilateral inscribed in a circle with centre O. If COD = 120 and BAC = 30, then BCD is: (a) 75 (b) 90 (c) 120 (d) Two chords AB and CD of a circle with centre O intersect each other at the point P. If AOD = 20 and BOC = 30, then BPC is equal to: (a) 50 (b) 20 (c) 25 (d) A straight line parallel to BC of ABC intersects AB and AC at points P and Q respectively. AP = QC, PB = 4 units and AQ = 9 units, then the length of AP is: (a) 25 units (b) 3 units (c) 6 units (d) 6.5 units 85. Two chords AB and CD of circle whose centre is O, meet at the point P and AOC = 50, BOD = 40. Then the value of BPD is (a) 60 (b) 40 (c) 45 (d) Two line segments PQ and RS intersect at X in such a way that XP = XR, If PSX = RQX, then one must have (a) PR = QS (b) PS = RQ (c) XSQ = XRP (d) ar( PXR) = ar( QXS) 87. In a ABC, = 2 and = 2 then ABC is: (a) 30 (b) 45 (c) 60 (d) In ABC, A + B = 145 and C + 2 B = 180. State which one of the following relations is true? (a) CA = AB (b) CA < AB (c) BC > AB (d) CA > AB Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 36

39 124. From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to diameter of the circle, then APB is (a) 45 (b) 90 (c) 30 (d) Two circles intersect at A and B. P is a point on produced BA. Pt and PQ are tangents to the circles. The relation of PT and PQ is (a) PT = 2PQ (b) PT < PQ (c) PT > PQ (d) PT = PQ 126. P and Q are two points on a circle with centre at O. R is a point on the minor are of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the point S. If PSQ = 20, then PRQ =? (a) 80 (b) 200 (c) 160 (d) PR is tangent to a circle, with centre O and radius 4 cm, at point Q. If POR = 90, OR = 5 cm and OP = cm, then (in cm) the length of PR is: (a) 3 (b) (c) (d) 128. The distance between the centre of two equal circles. Each of radius 3 cm, is 10 cm. The length of a transverse common tangent is (a) 8 cm (b) 10 cm (c) 4 cm (d) 6 cm 129. Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are point of contact and PAB = 35. Then ABP is (a) 35 (b) 55 (c) 65 (d) If a chord of a circle of radius 5 cm is a tangent to another circle of radius 3 cm, both the circles being concentric, then the length of the chord is (a) 10 cm (b) 12.5 cm (c) 8 cm (d) 7 cm 131. Two circles touch each other externally at point A and PQ is a direct common tangent which touches the circles at P and Q respectively. Then PAQ = (a) 45 (b) 90 (c) 80 (d) The tangents at two points A and B on the circle with centre O intersects at P; If in quadrilateral PAOB, AOB : APB = 5 : 1, then measure of APB is: (a) 30 (b) 60 (c) 45 (d) AB is a chord to a circle and PAT is the tangent to the circle at A. If BAT = 75 and BAC = 45, C being a point on the circle, then ABC is equal to (a) 40 (b) 45 (c) 60 (d) The tangents are drawn at the extremities of diameter AB of a circle with centre P. If a tangent circle with circle at the point C intersects the other two tangents at Q and R, then the measure of the QPR is (a) 45 (b) 60 (c) 90 (d) Point O is the circum centre of the triangle ABC. If BAC = 85 and BCA = 75 then the value of OAC is (a) 40 (b) 60 (c) 70 (d) In AD is angle bisector of A. If AB = 8 cm, AC = 10 cm & BC = 13.5 cm then find BD. (a) 8 cm (b) 7.5 cm (d) 6 cm (d) 6.5 cm 137. In an equilateral incentre, circumcentre and orthocentre are (a) Collinear (b) Coincident (c) Circular (d) Not related 138. What will be the value of x. (a) 15 0 (b) (c) 20 0 (d) 30 0 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 39

40 139. In ABC, ABC = 70, BCA = 40. O is the point of intersection of the perpendicular bisectors of the sides, then the angle BOC is (a) 100 (b) 120 (c) 130 (d) In the given figure, ONY = 50 and OMY = 15, Then the value of the MON is (a) 30 (b) 40 (c) 20 (d) In a circle of radius 21 cm, an arc subtends an angle of 72 at the centre. The length of the arc is (a) 21.6 cm (b) 26.4 cm (c) 13.2 cm (d) 19.8 cm 142. Two chords of lengths a metre and b metre sub end angles 60 and 90 at the centre of the circle respectively. Which of the following is true? (a) b = 2 a (b) a = 2 b (c) a=2b (d) b= 2a 143. The angle subtended by a chord at its centre is 60, then the ratio between chord and radius is (a) 1 : 2 (b) 1 : 1 (c) 2 : 1 (d) 2 : A chord 12 cm long is drawn in a circle of diameter 20 cm. The distance of the chord from the centre is (a) 8 cm (b) 6 cm (c) 10 cm (d) 16 cm 145. Two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally. If the perpendicular bisector of AB meets the bigger circle of AB meets the bigger circle in P and Q, then the value of PQ is (a) 6 cm (b) 2 6 cm (c) 3 6 cm (d) 4 6 cm 146. The length of the common chord of two circles of radii 30 cm and 40 cm whose centres are 50 cm apart, is (in cm) (a) 12 (b) 24 (c) 36 (d) Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is (a) 2r units (b) 3 r units (c) 5 r units (d) r units 148. Two circles C 1 and C 2 touch each other internally at P. Two lines PCA and PDB meet the circles C 1 In C, D and C 2 in A, B respectively. If BDC = 120, then the value of ABP is equal to (a) 60 (b) 80 (c) 100 (d) Two circles intersect each other at the points A and B, A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is (a) 1.50 cm (b) 2.25 cm (c) 4.50 cm (d) 9.00 cm 150. Two circles touch externally at P. QR is a common tangent of the circles touching the circles at Q and R. Then measure of QPR is (a) 60 (b) 30 (c) 90 (d) Chords AC and BD of a circle with centre O intersect at right angles at E. If OAB = 25, then the value of EBC is (a) 30 (b) 25 (c) 20 (d) In a circle of radius 17 cm, two parallel chords of length 30 cm and 16 cm are drawn. If both the chords are on the same side of the centre, then the distance between the chords is (a) 9 cm (b) 7 cm (c) 23 cm (d) 11 cm 153. Two chords AB and CD of a circle with centre O, intersect each other at P. If AOD = 100 and BOC = 70, then the value of APC is (a) 80 (b) 75 (c) 85 (d) 95 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 40

43 (a) (b) (c) (d) If in the given figure AB DC then find the value of ADC. (a) 70 0 (b) 60 0 (c) 45 0 (d) In a ABC, AD is bisector of A. If BD = 2.5 cm, AC = 4.2 cm, AB = 6 cm then DC =? (a) 2.1 (b) 3 cm (c) 1.2 cm (d) None of these 191. Two circles touch each other internally. If their radii are 2 cm & 3 cm. Find the length of that chord of larger circle which touches the smaller one. (a) 2 2 cm (b) 4 2 cm (c) 3 2 cm (d) None of these 192. ABCD is a rhombus whose side AB = 4 cm and ABC = 120, then the length of diagonal BD is equal to: (a) 1 cm (b) 2 cm (c) 3 cm (d) 4 cm 193. ABCD is a trapezium whose side parallel to. Diagonal and intersect at O. If = 3, = x 3, = 3x 19 and = x 5, the value (s) of x will be: (a) 7, 6 (b) 12, 6 (c) 7, 10 (d) 8, ABCD is a rhombus. AB is produced to F and BA is produced to E such that AB = AE= BF. Then: (a) ED > CF (b) ED CF (c) ED 2 + CF 2 = EF 2 (d) ED CF 195. The ratio of the angles A and B of a non-square rhombus ABCD is 4 : 5, then the value of C is: (a) 50 (b) 45 (c) 80 (d) In a quadrilateral ABCD, with unequal sides if the diagonals AC and BD intersect at right angles. Then (a) AB 2 + BC 2 = CD 2 + DA 2 (b) AB 2 + CD 2 = BC 2 + DA 2 (c) AB 2 + AD 2 = BC 2 + CD 2 (d) AB 2 + BC 2 = 2(CD 2 +DA 2 ) 197. ABCD is a rhombus. A straight line through C cuts AD produced at P and AB produced at Q. If DP = AB, then the ratio of the length of BQ and AB is (a) 2 : 1 (b) 1 : 2 (c) 1 : 1 (d) 3 : If PAB is an intersecting line which intersects the circle at points A & B. PT is a tangent then PA will be (a) PT 2 (b) PT (c) AT (d) None of these 199. AB is a diameter of a circle point P is on the circle. If PAB = 40 0 then find PBA. (a) 40 0 (b) 60 0 (c) 50 0 (d) None of these Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 43

45 (a) 10 cm (b) 12.5 cm (c) 8 cm (d) 7 cm 219. A shape formed after joining the respective mid-points of a quadrilateral is: (a) Rhombus (b) Square (c) Rectangle (d) None of these 220. In ABCD if AB = BC = CD = CA and AC BD, then this quadrilateral is a: (a) Trapezium (b) Square (c) Rhombus (d) None of these 221. The side AB of a parallelogram ABCD is produced to E in such way that BE = AB. DE intersects BC at Q. The point Q dives BC in the ratio (a) 1 : 2 (b) 1 : 1 (c) 2 : 3 (d) 2 : The length of the diagonal BD of the parallelogram ABCD is 18 cm. If P and Q are the centroid of the ABC and ADC respectively the length of the line segment PQ is (a) 4 cm (b) 6 cm (c) 9 cm (d) 12 cm 223. If all the sides of a parallelogram are equal and any one angle is 90 0 then this is a (a) Square (b) Rectangle (d) Trapezium (d) None of these 224. Two tangents QA & QB have been drawn from point Q to a circle, where AQB = Find APB. (a) 50 0 (b) 60 0 (c) 70 0 (d) Two equal circles intersect each other at two points. If length of the common chord is 10cm and the distance between centres is 6cm then find the radius of each circle. (a) 5.83 (b) 6.40 (c) 6.84 (d) BC is diameter of a circle of centre O, If AD bisects BAC then find BCD. (a) 90 0 (b)60 0 (c) 45 0 (d) The sum of the interior angles of a polygon is The number of sides of the polygon is (a) 6 (b) 9 (c) 10 (d) The sum of interior angles of a regular polygon is The number of sides of the polygon is (a) 10 (b) 12 (c) 6 (d) Among the angles 30, 36, 45, 50 one angle cannot be an exterior angle of a regular polygon. The angle is (a) 30 (b) 36 (c) 45 (d) If each interior angle of a regular polygon is 150, the number of sides of the polygon is (a) 8 (b) 10 (c) 15 (d) ) None of these 231. Each interior angle of a regular polygon is 144. The number of sides of the polygon is (a) 8 (b) 9 (c) 10 (d) If the sum of the interior angles of a regular polygon be 1080, the number of sides of the polygon is (a) 6 (b) 8 (c) 10 (d) An interior angle of a regular polygon is 5 times its exterior angle. Then the number of sides of the polygon is (a) 14 (b) 16 (c) 12 (d) If the ratio of an external angle and an internal angle of a regular polygon is 1 : 17, then the number of sides of the regular polygon is (a) 20 (b) 13 (c) 36 (d) Ratio of the number of sides of two regular polygons is 5 : 6 and the ratio of their each interior angle is 24 : 25. Then the number of sides of these two polygons is (a) 20, 24 (b) 15, 18 (c) 10, 12 (d) 5, In a regular polygon if one of its internal angle is greater than the external angle by 132, then the number of sides of the polygon is (a) 14 (b) 12 (c) 15 (d) If the sum of interior angles of a regular polygon is equal to two times the sum of exterior angles of that polygon, then the number of sides of that polygon is (a) 5 (b) 6 (c) 7 (d) There are two regular polygons with number of sides equal to (n 1) and (n + 2). Their exterior angles differ by 6. The value of n is (a) 14 (b) 12 (c) 13 (d) 11 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 45

46 239. The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively (a) 6, 12 (b) 5, 10 (c) 4, 8 (d) 7, The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is (a) 10 (b) 8 (c) 12 (d) Measure of each interior angle of a regular polygon can never be: (a) 150 (b) 105 (c) 108 (d) Each internal angle of regular polygon is two times its external angle. Then the number of sides of the polygon is: (a) 8 (b) 6 (c) 5 (d) The number of sides in two regular polygons are in the ratio 5 : 4 and the difference between each interior angle of the polygons is 6. Then the number of sides is: (a) 15, 12 (b) 5, 4 (c) 10, 8 (d) 20, The difference between the exterior and interior angles at a vertex of a regular polygon is 150. The number of sides of the polygon is (a) 10 (b) 15 (c) 24 (d) In a regular polygon, the exterior and interior angles are in the ratio 1: 4 The number of sides of the polygon is (a) 10 (b) 12 (c) 15 (d) Each interior angle of a regular polygon is three times is three times its exterior angle, then the number of sides of the regular polygon is: (a) 9 (b) 8 (c) 10 (d) A parallel line has been drawn parallel to each side from each vertex of a What will be the ratio of perimeter of new and the old (a) 3 : 2 (b) 4 : 1 (c) 2 : 1 (d) 2 : In ABC, the internal & external bisectors of B & C meet at P & Q respectively then PBQ PCQ? (a) (b) (c) (d) In given figure AB CD then find the value of (a) (b) (c) (d) In the given figure AD BC & internal bisectors of B and A meet at point O. Find the measure of AOB in degree. (a) 90 0 (b) (c) (d) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 46

47 251. Inside a square ABCD, BEC is an equilateral triangle. If CE and BD intersect at O, then BOC is equal to (a) 60 (b) 75 (c) 90 (d) ABCD is a parallelogram, its diagonals AC and BD intersect each other at point O. DAC = 32 0 and AOB = 70 0 then find DBC. (a) 30 0 (b) (c) 38 0 (d) ABCD and ADEF are parallelograms in the given figure. If CA = AF and ACD = 60 0 then DECF =? (a) 30 0 (b) 60 0 (c) 75 0 (d) In the figure given below, if x y z then find the value of A and B. (a) (b) 160 0, 20 0 (c) 130 0, 30 0 (d) None of these 255. In the figure given below, line AB and CD intersect each other at point O. If AOC = 125 0, find the value of BOD (a) 65 0 (b) 55 0 (c) (d) Q is a point in the interior of a rectangle ABCD. If QA = 3 cm, QB = 4 cm and QC = 5 cm, then the length of QD (in cm) is (a) 3 2 (b) 5 2 (c) 34 (d) 4 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 47

48 257. If the opposite sides of a quadrilateral and also its diagonals are equal, then each of the angles of the quadrilateral is (a) 90 (b) 120 (c) 100 (d) ABCD is a rectangle where the ratio of the length of AB and BC is 3 : 2. If P is the mid-point of AB, then the value of sin CPB is (a) (b) (c) (d) 259. In the figure given below POR and QOR from a linear pair. If a B = 80 0, then find the value of a and b. (a) 140 0, 40 0 (b) 130 0, 50 0 (c) 160 0, 20 0 (d) 120 0, The length of the sides forming the right angle in a right angled triangle is a and b. Three squares are inscribed outwards on the three sides of the triangle. What is the total sum of the area of the triangles and that of the squares so formed? (a) 2(a 2 + b 2 ) + ab (b) 2(a 2 + b 2 ) ab (c) 2(a 2 + b 2 ) ab (D) 2.5(a 2 + b 2 ) 261. What is the point of concurrent of altitudes in a triangle called (a) Circumcentre (b) Othocentre (c) Incentre (d) Centroid 262. AC is the diameter of the circumcircle of the cyclic quadrilateral ABCD. If BDC = 42 0, then the measure of ACB is (a) 42 0 (b) 45 0 (c) 48 0 (d) The perimeters of two similar triangles ABC and PQR are 36 cm and 24 cm respectively. If PQ = 10 cm. then AB is (a) 15 cm (b) 12 cm (c) 14 cm (d) 26 cm 264. In ABC. Two points D and E are taken on the lines AB and BC respectively in such a way that AC is parallel to DE. Then ABC and DBE are (a) similar only if D lies outside the line segment AB (b) congruent only if D lies outside the line segment AB (c) always similar (d) always congruent 265. In PQR, S and T are points on sides PR and PQ respectively such that PQR = PST. If PT = 5 cm, PS = 3 cm and TQ = 3 cm, then length of SR is (a) 5 cm (b) 6 cm (c) cm (d) cm 266. In ABC and DEF, AB = DE and BC = EF. Then one can infer that ABC DEF, when (a) BAC = EDF (b) ACB = EDF (c) ACB = DFE (d) ABC = DEF 267. Point O is the in centre of 3 (a) 100 (b) 105 (c) 110 (d) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 48

49 In the above figure, O is the cnetre of the circle, OA = 3 cm, AC = 3 cm and OM AC then ABC is (a) 60 0 (b) 45 0 (c) 30 0 (d) None of these 269. In the given figure PQ RS, then NMS is equal to (a) 20 0 (b) 23 0 (c) 27 0 (d) Which angle of the following is equal to two third of its complements? (a) 36 0 (b) 45 0 (c) 48 0 (d) In the given figure AB CD. If BAF = 98 0 and AFC = 144 0, then the value of ECD is (a) 62 0 (b) 64 0 (c) 82 0 (d) In ABC, A = 90 and AD BC where D lies on BC. If BC = 8 cm, AC = 6 cm, then ABC : ACD =? (a) 4 : 3 (b) 25 : 16 (c) 16 : 9 (d) 25 : In a right-angled triangle ABC, ABC = 90, AB = 5 cm and BC = 12 cm. The radius of the circum-circle of the triangle ABC is (a) 7.5 cm (b) 6 cm (c) 6.5 cm (d) 7 cm Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 49

51 In the figure drawn above AB CD. If DCE = x and ABE = y, then the measure of CEB is] (a) y x (b) (x + y)/2 (c) x + y ( /2) (d) x + y 294. In the figure drawn above LM QR. If PQR is divided by LM in such a way that the area of trapezium LMRQ is twice the area of PLM, then will be equal to (a) (b) (c) (d) 295. Let there be two points A and B. What is the locus of point P, such that APB = 90 0? (a) The line segment AB itself (b) The point P itself. (c) The circumference of the circle with AB as its diameter. (d) The right bisector of AB The two medians AD and BE of a triangle ABC intersect each other at point G making right angle. If AD = 9 cm and BE = 6 cm then the length of BD is (a) 10 cm (b) 6 cm (c) 5 cm (d) 3 cm 297. I is the incentre of ABC, ABC = 60 and ACB = 50. Then BIC is: (a) 55 (b) 125 (c) 70 (d) I is the incentre of a triangle ABC. If ABC = 65 and ACB = 55, then the value of BIC is (a) 130 (b) 120 (c) 140 (d) If two angles of a triangle are 21 and 38, then the triangle is (a) Right-angled triangle (b) Acute-angled triangle (c) Obtuse-angled triangle (d) Isosceles triangle 300. A man goes 24 m due west and then 10 m due north. Then the distance of him from the starting point is (a) 17 m (b) 26 m (c) 28 m (d) 34 m 301. The side of a triangle are in the ratio 3 : 4 : 6. The triangle is: (a) acute-angled (b) right-angled (c) obtuse-angled (d) either acute-angled or right-angled 302. In ABC, C is an obtuse angle. The bisectors of the exterior angles at A and B meet BC and Ac produced at D and E respectively. If AB = AD = BE, then ACB = (a) 105 (b) 108 (c) 110 (d) If the length of the sides of a triangle are in the ratio 4 : 5 : 6 is 3 cm, then the altitude of the triangle corresponding to the largest side as base is: (a) 7.5 cm (b) 6 cm (c) 10 cm (d) 8 cm 304. The sum of three altitudes of a triangle is (a) equal to the sum of three sides (b) less than the sum of sides (c) greater than the sum of sides (d) twice the sum of sides Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 51

53 (a) (b) (c) (d) 324. In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is (a) 120 (b) 60 (c) 30 (d) ABC is an isosceles triangle with AB = AC. A circle through B touching AC at the middle point intersects AB at P. Then AP : AB is: (a) 4 : 1 (b) 2 : 3 (c) 3 : 5 (d) 1 : A, B, C are three points on a circle. Tangent drawn at point A intersects BC (when produced) at point T. BTA = 40 0, CAT = Then the measure of the angle subtended by BC at the centre of the circle is (a) 84 0 (b) 92 0 (c) 96 0 (d) Which one of the following values can never be the measure of an internal angle of a regular polygon? (a) (b) (c) (d) The two chords AB and AC are 8 cm and 6 cm long respectively. If BAC = 90 then radius of the circle is (a) 25 cm (b) 20 (c) 4 cm (d) 5 cm 329. In 2 3 (a) 6cm (b) 9 cm (c) 12 cm (d) 8 cm 330. G is the centroid of the equilateral ABC. If AB = 10 cm then length of AG is (a) cm (b) cm (c) 5 3 cm (d) 10 3 cm 331. If the circum radius of an equilateral triangle be 10 cm, then the measure of its in - radius is (a) 5 cm. (b) 10 cm. (c) 20 cm. (d) 15 cm If the three medians of a triangle are same then the triangle is (a) equilateral (b) isosceles (c) right angled (d) obtuse - angle 333. The radius of the incircle of the equilateral triangle having each side 6 cm is (a) 2 3 cm (b) 3 cm (c) 6 3 cm (d) 2 cm 334. ABC is an equilateral triangle and CD is the internal bisector of C. If DC is produced to E such that AC = CE, then CAE is equal to (a) 45 (b) 75 (c) 30 (d) Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is (a) AX = BY = CZ (b) AX BY = CZ (c) AX = BY CZ (d) AX BY CZ 336. If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then. (a) PQR must be an equilateral triangle (b) PQ + QR + PR = AB (c) PQ + QR + PR = 2 AB (d) PQR must be a right angled triangle 337. In a triangle, if orthocentre, circumcentre, incentre and centroid coincide, then the triangle must be (a) obtuse angled (b) isosceles (c) equilateral (d) right angled 338. If the in centre of an equilateral triangle life inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is (a) 9 3 cm (b) 6 3 cm (c) 3 3 cm (d) 6 cm 339. The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of PSR is (a) 30 (b) 15 (c) 60 (d) If ABC is an equilateral triangle and D is a point on BC such that AD BC, then (a) AB : BD = 1 : 1 (b) AB : BD = 1 : 2 (c) AB : BD = 2 : 1 (d) AB : BD = 3 : The in-radius of an equilateral triangle is of length 3 cm. The length of each of its medians is (a) 12 cm (b) cm (c) 4 cm (d) 9 cm 342. In a triangle, if three altitudes are equal, then the triangle is (a) Obtuse (b) Equilateral (c) Right (d) Isosceles 343. If in a triangle, the circumcentre, in centre, centroid and ortho centre coincide, then the triangle is (a) Acute angled (b) Isosceles (c) Right angled (d) Equilateral Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 53

55 (a) 2 : 1 (b) 1 : 2 (c) 1 : 1 (d) 3 : A line drawn parallel to BC in intersects its side AB and AC at point D and E respectively. If area of ABE is 36 cm 2 then the area of is (a) 18 cm 2 (b) 36 cm 2 (c) 18cm (d) 36 cm 363. Two chords AB and CD of a circle with centre O, meet at point P. If AOC 50 4 (a) 60 (b) 40 (c) 45 (d) ABCD is a square Point M and N are mid points of the side AB and BC respectively. DM and AN intersect at point O. Then which of the following is correct? (a) OA : OM = 1 : 2 (b) AN = MD (c) ADM = ANB (d) AMD = BAN 365. If the value of P + (a) 4 (b) 5 (c) 10 (d) x, x + 1 and x 1 are the sides of a right angled then its hypotenuse will be: (a) 5 (b) 4 (c) 1 (d) If the sum of the interior angles of a polygon is , find the number of its sides (a) 8 (b) 6 (c) 10 (d) The sum of the interior angles of a polygon is the number of sides of the polygon is (a) 15 (b) 18 (c) 20 (d) If the sum of the internal angles of a polygon is then the number of the sides of the polygon is (a) 8 (b) 10 (c) 12 (d) In adjoining figure DEC = 70 0, BC DE and CBA = If BAC = x 0 then find the value of x. (A) 30 0 (b) 26 0 (c) 18 0 (d) In the figure, CE BD and BAD = 110 0, ABD = 30 0, ADC = 75 = 60 0, then what will be the value of x? (a) 45 0 (b) 75 0 (c) 85 0 (d) In the adjoining figure PQA = 20 0 and APQ = then find the value of PAQ. Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 55

56 (a) (b) 40 0 (c) 20 0 (d) In the given figure A = 60 0 and ABC = 80 0, then BPC is (a) 40 0 (b) 45 0 (c) 20 0 (d) If each interior angle of a regular polygon is then find the number of sides (a) 6 (b) 8 (c) 5 (d) OA and OB are radii of a circle with centre O AOB 2 0. Tangents drawn at points A and B meet at point C. If OC divides the circle into two equal parts at point D then point D divides the side OC in the ratio of (a) 1 : 2 (b) 1 : 3 (c) 1 : 1 (d) 2 : In the figure AB CD, BAE = 105 0, AEC = 25 0 then DCE is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 56

57 (a) (b) 80 0 (c) (d) In the given ROQ is a diameter. If POR = then QPO is (a) 40 0 (b) 45 0 (c) 50 0 (d) In adjoining figure CAB = 90 0 and AD BC. If AC = 100 cm, AB = 100 cm and BC = 125 cm, then the length of CD is (a) 50 cm (b) 37.5 cm (c) 62.5 cm (d) 65 cm 379. In the adjoining figure AOB = 90 0 then APB is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 57

58 (A) 30 0 (b) 45 0 (c) 25 0 (d) data insufficient 380. In the adjoining figure BAT = 65 0, then find BDA. (a) 65 0 (b) (c) (d) In acute angled If O is the orthocentre of (a) (b) (c) 60 0 (d) In the adjoining figure, OAB = 20 0, OCB = 30 0 then the value of AOC is (a) 80 0 (b) (c) 50 0 (d) AB and CD are the diameters of circle C (O, r). if OBD = 50 0 then find the value of AOC. (a) 80 0 (b) 40 0 (c) (d) In the adjoining figure ABC = 45 0, then CDT is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 58

59 (a) 15 0 (b) 20 0 (c) 25 0 (c) In the given figure AB CD, EFC = 30 0 and ECF = 100 (a) (b) 70 0 (c) (d) The areas of two similar triangles are 96 cm 2 and 150 cm 2. If the largest side of the larger triangle is 20 cm the largest side of the smaller triangle is (a) 15 cm (b) 16 cm (c) 18 cm (d) 20 cm 387. The area of a rhombus is 120cm 2. If the length of one of its diagonal is 10 cm, the length of its one side is (a) 12 cm (b) 13 cm (c) 24 cm (d) 2 3 cm 388. In the given figure ABC = (a) 80 (b) 60 0 (c) 40 0 (d) In the adjoining AB is the diameter of a circle. BOD = 15 0 and EOA = 85 0, then ECA is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 59

60 (a) 20 0 (b) 35 0 (c) 40 0 (d) None of these 390. In 6 is the mid point of AC. Find the length of BC. (A) 4 cm (b) 6 (c) 3 cm (d) 3.5 cm 391. In the given figure ADC = 140 and AOB is the diameter of the circle then BAC is (a) 40 0 (b) 50 0 (c) 70 0 (d) In the given figure QPR = 67 2 is the diameter of the circle, then QRS is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 60

61 (a) 41 0 (b) 23 0 (c) 67 0 (d) In the given figure PQRS is a rectangle, whose area is 8 cm 4 cm. Triangle are equilateral and the radii of each circle is 1 cm. Then the perimeter of ABCDEFGHIJKLMNA is (a) cm (b) cm (c) cm (d) cm 394. The vertex A of a vertical pillar is at the ground. C is the midpoint of AB. BC subtends an angle tan (a) (b) (c) (d) 395. A, B, C are points such that AB = 10 cm and BC = 6 cm. Then AC is (a) 2 cm (b) 3 cm (c) 5 cm (d) 16 cm 396. ABCD is a parallelogram. If E and F are two points on sides DC and AD respectively. If areas of respectively, then Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 61

62 (a) (b) 2 (c) 2 (d) If PL, QM and RN are altitudes of O is the orthocentre of PQR, then Q will be the ortho centre of (a) (b) PRn (c) (d) 398. In an isosceles ABC, a perpendicular is drawn through the point P on BC, it intersect AB at Q, and meet CA at R when CA is produced to R. then (a) AQR is equilateral (b) AQR is isosceles (c) Q is the mid point of AB (c) A is the midpoint of CR 399. The ratio of the internal and the external angle of a regular polygon is 2 : 1. The number of the sides of the polygon is (a) 3 (b) 5 (c) 6 (d) In the following figure the area of the equilateral triangle inscribed in the square of side a will be (a) a 2 (b) (c) Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 62 (d) 401. The interior bisector of B and C of then the value of BOC is (a) 50 0 (b) (c) (d) In ABC the medians BE and CF intersect at point G. If the straight line AGD, intersect BC at point D such that GD = 1.5 cm then the length of AD is (a) 2.5 cm (b) 3 cm (c) 4 cm (d) 4.5 cm 403. Three lines OA OB and OC are drawn through point O If OP and OQ are the bisector of BOA and AOC respectively and POQ 0, then a BOC is an obtuse angle b BOC is an acute angle c BOC is a straight line d BOC is a right angle 404. In the adjacent figure, O is the centre of the circle. If tangent PQ = 12 lcm and BQ = 8 cm. Then the length of chord AB is

63 (a) 10 cm (b) 4 5 cm (c) 4 cm (d) 18 cm 405. The radii of two non intersecting circles are R and r and one circle is inscribed inside the other circle. If the least distance between their circumference is S then the distance (a) R r + s (b) R r s (C) R + r s (d) R r 406. In intersect at O and BE + EO = Bo, then (a) CO + OF = CF (b) CF + FO = CO (c) FC CO = FO (d) CF + FO = CO 407. If midpoint of the sides BC, CA and AB of and BE intersect at point G inside the (a) CG + GF > CF (b) CG + GF < CF (c) CG + GF = CF (d) CG = GF = 408. The radii of two circles are 15 cm and 20 cm respectively. Their centres are at a distance of 25 cm. Find the common length of the common chord. (a) 24 cm (b) 25 cm (c) 15 cm (d) 20 cm 409. A line XY drawn parallel to the BC the base of meet AB and AC at point X and Y respectively. If AB = 5 BX and YC = 3 cm, then AY is (a) 8 cm (b) 15 cm (c) 10 cm (d) 12 cm 410. In triangle ABC, D, E, F are the mid points of sides AB, BC and CA respectively. If the area of then the area of DEF is (a) (b) (c) (d) 411. What will be the length of the chord that subtends an angle of 90 0 at the cnetre of a circle with the radius of unit length? (a) 2 (b) 3 (c) (d) 412. A circle C passes through three non-collinear points D, E and F. Where DE = EF = DF = 3 cm. Then the radius of the circle is (a) (b) 3 (c) cm (d) 413. In circle, a square and an equilateral triangle have been inscribed. If their sides are a and b, respectively. Then (a) a 2 = (b) (c) 3b 2 = 2a 2 (d) 3a 2 = 2b In If AD BC then BC AD is (a) BD.AC (b) AB.CD (c) AB.AC (d) AC.BC 415. In the given figure ABC = 90 6 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 63

65 (a) 2(a + (b) (c) 2a + (d) 427. If D, E and F are the mid point of the side BC, AC and AB of an equilateral triangle ABC. Then the ratio of the areas of (a) 1.1 : 1 (b) 1 : 1.1 (c) 0.9 : 1 (d) 1 : ABCD is a cyclic quadrilateral tangents drawn at A and C meet at P If ABC 0 then APC will be (a) 20 0 (b) 40 0 (c) 60 0 (d) A parallelogram ABCD and a rectangle ABEF are drawn between parallel lines EF and CD. If AB = 7cm and BE = 6.5 cm, then area of parallelogram will be (a) 22.75cm 2 (b) cm 2 (c) 45.5 cm 2 (d) 45.0 cm In BE intersect at G, then AG + BG + CG is equal to (a) AD = BE = CF (b) (AD + BE + CF) (c) (d) 431. In (a) p 2 = b 2 + c 2 (b) (c) (d) p 2 = b 2 c The area of 6 2. XY is drawn parallel to BC which divides AB in the ratio 3 : 5. If BY is joined then area of (a) 3.5 cm 2 (b) 3.7 cm 2 (c) 3.75 cm 2 (d) 4.0 cm D is a point on the side AB of ADE ACB then the value of AD.AB is (a) AE. BC (b) AC.DE (c) AE.AC (d) AB.BC 434. In the adjoining figure AB CD and EF transverse them at point M and N The bisector of M and N meet at point Q If AME 0, find the value of MQN Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 65

66 (A) 60 0 (b) 70 0 (c) 80 0 (d) In a plane there are three concurrent lines OA OB and OC and their point of concurrence is O If AOB BOC and COA measure 2x 0, 5x 0 and 8x 0 respectively then the value of x is (a) 24 0 (b) 18 0 (c) 15 0 (d) In the adjoining figure AB is the diameter C and D are points on the circle If CAD 3 0 CBA 0, then find the value of ACD (a) 40 0 (b) 50 0 (c) 35 0 (d) In A meets with BC at D If AB 4 AC 3 and A 6 0, then the length of AD will be (a) 2 3 (b) (c) (d) 438. In the adjoining figure, a rectangle is inscribed in a circle with centre O. AB > BC The ratio of the area of circle to that of the rectangle is 3 Line segment DE intersect AB at point E where ODC ADE Then AE AD =? Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 66

67 (a) 1 : 3 (b) 1 : 2 (c) 1 : 2 3 (d) 1 : In the adjoining figure ABCD is a rectangle in which AE = EF = FB. Then the ratio of the areas of (a) 1 : 4 (b) 1 : 6 (c) 2 : 5 (d) 2 : In adjoining figure in 4 BP and CP are the bisector of B and C respectively. Then BPC is (a) 90 0 (b) (c) (d) In the adjoining figure if AB BC CD DE EF FG GA then the approximate value of DAE is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 67

68 (a) 15 0 (b) 20 0 (c) 30 0 (d) In the adjoining figure AB is the diameter and the length of the radius is 6.5 cm. If the length of the chord CA is 5 cm, find the area of (a) 60 cm 2 (b) 30 cm 2 (c) 40 cm 2 (d) 52 cm In the adjoining figure ABCD is a square and BCE is an equilateral triangle Then the value of DEC is (a) 15 0 (b) 30 0 (c) 20 0 (d) In the adjoining figure OG = OF, then the area of the figure will be (a) 64m 2 (b) 62m 2 (c) 60m 2 (d) 58m In quadrilateral ABCD, the line segment DE and CE are the bisectors of C and D respectively then the right answer is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 68

69 (a) A + B = CED (b) A + B = 2 CED c A B 3 CED (d) None of these 446. ABCD is a parallelogram; There is a point P on side AB. If DP and CP are joined in such a way that they bisect ADC and BCD respectively. Then DC is equal (a) CB (b) 2 CB (c) 3 CB (d) 4 CB 447. In the given figure AD = BD = AC; CAE = 75 (a) 45 0 (b) 50 0 (c) 60 0 (d) in the given figure EC BA, ECD = 70 2 (a) 20 (b) 50 0 (c) 60 0 (d) If in a triangle ABC, a line is drawn parallel to BC from a point D on AB which intersects AC at E. Then which of the following statements is not true? (a) AD : DE = AB : BC (b) (c) ar ( 2 (d) 450. If AD : CB = 2 : 3 and OA : OC = 4 : 7 then find OD : OB Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 69

70 (a) 4 : 7 (b) 12 : 14 (c) 7 : 4 (d) 14 : Let ABCD be a square. M, N, R are points on AB, BC and CD respectively, such that AM = BN = CR. If MNR = 90 0 then MRN is (a) 30 0 (b) 45 0 (c) 60 0 (d) In the adjoining figure PR AB, PQ BC and QR CA. The find the relation between AC and QR. (a) AC = QR (b) 2 AC 2 = QR 2 (c) AC = BQ.QR (d) AC.QR = ABC is a triangle. A point P is on AB such that ACP = ABC. If AC = 9 cm, CP = 12 cm and BC = 15 cm, then AP is (a) 11.2 cm (b) 10.2 cm (c) 8.0 cm (d) 7.2 cm 454. In the adjoining figure, in = 3 AP, CQ = 3 AQ and BC = 36. Find the value of PQ. (a) 6 (b) 8 (c) 9 (d) Let a triangle. In as OB and OC are the bisector of B and C respectively. If BAC = 60 0 then BOC is (a) (b) (c) (d) ABCD is a horizontal square. The diagonals of the square intersect at O. A 40 cm long rod OP is vertically situated at O. If the side of the square is 20 cm, then length of side PA is (a) 28.3 cm (b) 35.6 cm (c) 42.3 cm (d) 44.4 cm 457. In the adjoining figure the value of x is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 70

71 (a) 30 0 (b) 45 0 (c) 60 0 (d) None of these 458. In the adjoining figure, if AP = 6 cm, AB = 2 cm, PC = 8 cm then the length of CD (a) 4 cm (b) 3 cm (c) 5 cm (d) 6 cm 459. In a circle with centre C, PQ and RS are two parallel chords such that PQ = 8 cm and RS = 16 cm. If the chords are in the same side of the centre and distance between them is 4 cm. Find the radius of the circle. (a) 3 2 cm (b) 3 5 cm (c) 4 5 cm (d) 5 5 cm 460. In an equilateral triangle is drawn in a circle, then the ratio of a side fo the triangle and the diameter of the circle is (a) 2 2 (b) 3 2 (c) 1 : 3 (d) 2 : In the adjoining figure If PQ = 13 cm, AB = 6 cm, BR = 8.2 cm and PR = 5.2 cm then the lengths of QR and AR are (a) 8.2 cm and 10.4 cm (b) 4.1 cm and 6 cm (c) 2.6 cm and 5.2 cm (d) 4.1 cm and 10.4 cm 462. In the given figure O is the centre of the circle BAC = 52 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 71

72 (A) 52 0 (b) (c) (d) In the adjoining O is the centre of the circle. If PA = 12 cm, PC = 15 cm and CD = 7 cm, then find the length of AB. (a) 5 cm (b) 10 cm (d) 2 cm (d) 9 cm 464. In (a) 60 0 (b) 70 0 (c) 80 0 (d) None of these 465. A secant drawn from an external point O, intersects the circle at A and B such that OA = 4 cm and OB = 9 cm. Find the length of the tangent drawn from this point on the circle. (a) 3 (b) 5 cm (c) 6 cm (d) 466. In the given figure AB CD, ABO = 40 3 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 72

73 (a) 35 (b) (c) 70 0 (d) In the adjoining figure find the value of ABC. (A) 80 0 (b) 60 0 (c) 20 0 (d) In the adjoining figure AD is the bisector of BAC then AB is (a) 6 cm (b) 5 cm (c) 5.25 cm (d) 5.75 cm 469. If A and B are fixed points and a point P moves in such a way that APB is a right angle then the locus of the point P is (a) None of these (b) A circle (c) An ellipse (d) SA hyperbolic circle 470. In an equilateral (a) 2 AB 2 = 3 AD 2 (b) 3 AB 2 = 4 AD 2 (c) 5 AB 2 = 6 AD 2 (d) 4 AB 2 = 5 AD In the adjoining figure two chords AB and CD intersect at point P. If AB = 5 cm and PD = 4 cm, then what will be the length of CD? Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 73

74 (a) 4 cm (b) 3 cm (c) 2.5 cm (d) 2 cm 472. In the given figure AB CD, ALC = 60 and EC is the bisector of LCD. If EF AB then the value of CEF is (A) (b) (c) (d) None of these 473. Two chords AB and CD of a circle intersect each other at point E such that AE = 2.4 cm, BE = 3.2 cm and CE = 1.6 cm. Then length of DE is (a) 4.8 cm (b) 6.4 cm (d) 1.6 cm (d) 3.2 cm 474. Two equal circles with radius r intersect in such a way that they pass through the centre of each other. Find the length of the common chord. (a) r 3 (b) 3 (c) (d) r In the adjoining figure, ABC is an equilateral (a) 40 0, (b) 30 0, (c) 90 0, 90 0 (d) 60 0, A secant drawn from an external point O, intersect the circle at A and B, such that OA = 4cm, OB = 9 cm. Then what will be the length of the tangent drawn from this point on the circle? (a) 3 (b) 5 (c) 6 cm (d) 477. In the adjoining figure find the value of QSR Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 74

75 (a) 50 0 (b) 65 0 (c) 70 0 (d) In the adjoining figure in 0 and A = 2x 20 0, then the value of B is (a) 30 0 (b) 40 0 (c) 44 0 (d) In the adjoining figure PQ is the tangent and QOR is the diameter of a circle. If QPO = 35 0 then value of POR is (a) (b) (c) 70 0 (d) In the adjoining figure AB is the diameter and C and D are points on the circle. If CAD = 30 0 and CBA = 70 0 then what will be the value of ACD? (a) 40 0 (b) 50 0 (c) 35 0 (d) In the adjoining figure A, B, C and D are four points on the circle. If AB = 24, BC = 12 then what will be the ratio of the areas of Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 75

76 (a) 1 : 4 (b) 1 : 2 (c) 1 : 3 (d) data insufficient 482. In the adjoining figure the value of x is (a) 6 cm (b) 7 cm (c) 6.7 cm (d) 7.7 cm 483. In the given ABCD is a cyclic quadrilateral and O is the centre of the circle. If BOC = 136 0, then what will be the value of BDC (a) (b) (c)109 0 (d) None of these 484. In the given figure o is the centre of the circle. 25 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 76

77 (a) 25 (b) 30 (c) 65 (d) In the given figure PQ = 12 cm, BQ = 8 cm then the length of the chord is (a) 10 cm (b) 4 5 cm (c) 4 cm (d) 18 cm 486. In the given figure O is the centre of the circle. If AOC = then the value of ABC is (a) (b) (c) (d) What will be the value of x in the given figure? Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 77

78 (a) 40 0 (b) 25 0 (c) 30 0 (d) In the given figure O is the centre of the circle. If AB = 16 cm, CP = 6 cm, PD = 8 cm and AP > PB then value of AP is (A) 12 cm (b) 24 cm (c) 8 cm (d) 6 cm 489. In the given figure O is the centre of the circle then value of x is (a) 60 0 (b) 45 0 (c) 15 0 (d) If O is the centre of the circle, then value of x is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 78

79 (a) 35 0 (b) 30 0 (c) 39 0 (d) In the given figure ADB is (a) (b) (c) 48 0 (d) In the given figure the value of x is (a) 13 cm (b) 12 cm (d) 16 cm (d) 15 cm 493. In the given figure find the value of x Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 79

80 (a) 16 cm (b) 9 cm (d) 12 cm (d) 7 cm 494. In the given the value of x is (a) 2.2 cm (b) 1.6 cm (c) 3 cm (d) 2.6 cm 495. A polygon has 27 diagonals. Find the number of its sides (a) 9 (b) 10 (d) 11 (d) In the given figure BT and CT are two tangents then A is (a) 80 0 (b) 60 0 (c) 50 0 (d) If ABCD is a cyclic quadrilateral then value of x is Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 80

81 (a) (b) 80 0 (c) 70 0 (d) In the given figure, the value of x is (a) 60 0 (b) 90 0 (c) 70 0 (d) In the given figure O is the centre of the circle then ACB is (a) 60 0 (b) (c) 75 0 (d) In the given AD, AE and BC are tangents Then Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 81

82 (a) AD = AB + BC + CA (b) 2AD = AB + BC + CA (c) 3 AD = AB + BC + CA (d) 4 AD = AB + BC + CA 501. If the chord of a circle is equal to its radius the angle subtended by the chord at the centre of the circle is (a) 60 0 (b) 45 0 (c) 30 0 (d) AB is the diameter of the circle and O is its centre. CD and AB intersect in such a way that OE = EB and CE = 6 cm, ED = 2 cm. Find the radius of the circle. (a) 4 cm (b) 6 cm (c) 4 3 cm (d) 8 cm 503. AB is the diameter and AC is a chord of a circle and BAC = 30 0 then which of the statements is correct? Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 82

83 (a) BC > BD (b) BC > BD (c) BC = BD (d) Cannot say 504. In the given figure A, B, C are points on the circumference of the circle and O is the centre. If ABC is (a) 60 0 (b) 75 0 (c) 90 0 (d) None of these 505. In the given figure AD : DC = 2 : 3 then ABC is (a) 30 (b) 40 (c) 45 (d) In the given figure PQ is a tangent at point K, and LN is the diameter. If KLN = 30 (a) 30 0 (b) 50 0 (c) 60 0 (d) If the angles of a pentagon are in the ratio 1 : 2 : 3 : 5 : 9, then what is the value of the least smallest) angle? Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 83

84 (a) 72 0 (b) 45 0 (c) 54 0 (d) ABCD is a parallelogram and E is the midpoint of BC then (a) AF = AB (b) AF = 2 AB (c) AF = 3 AB (d) AF 2 = 2 AB The ratio of the corresponding sides of two similar triangles is 1 : 3. What will be ratio of their corresponding altitudes? (a) 1 : 3 (b) 3 : 1 (c) 1 : 9 (d) 9 : In the given figure XY AC, and XY divides the triangle into two equal parts. Then (a) (b) (c) (d) 511. ABCD and DEC are a square and an equilateral triangle respectively. Then DAE is (a) 45 0 (b) 30 0 (c) 15 0 (d) In the given figure AM BC and AN is the bisector of A. Then MAN will be- (If B = 65 0, C = 33 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 84

85 (a) 33 (b) 16 (c) 16 0 (d) What will be the number of diagonals in a regular hexagon? (a) 6 (b) 4 (d) 11 (d) What will be the ratio of the sum of the interior angles and that of the exterior angles of an octagon? (a) 1 : 2 (b) 1 : 3 (c) 2 : 3 (d) 3 : In the given figure AB CD then FXE is (a) 30 (b) 50 (c) 60 (d) The remainder after dividing 2x 3 3x 2 + 4x 1 by (x 1) will be (a) 10 (b) 2 (c) 1 (d) 10 Pinnacle SSC Coaching Centre, Gurudwara Road, Model Town, Hisar Page 85

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