Objective Mathematics

Size: px
Start display at page:

Download "Objective Mathematics"

Transcription

1 . In BC, if angles, B, C are in geometric seq- uence with common ratio, then is : b c a (a) (c) 0 (d) 6. If the angles of a triangle are in the ratio 4 : :, then the ratio of the longest side to the perimeter is : (a) : ( ) : (c) : ( ) (d) :. Let BC and BC' be two non-congruent triangles with sides B = 4, C = C' = and angle B = 0º. The absolute value of the difference between the area of these triangles is : (a) 8 4 (c) 6 (d). In an isosceles triangle if one angle is 0º and radius of its incircle is square units is :, then area of the triangle in (a) 7 7 (c) 7 (d) 4 4. If a, b and c denote the length of the sides opposite to angles, B and C of a triangle BC, then the correct relation is given by : B C (a) ( b c)sin a cos B C ( b c)cos asin B C (c) ( b c)cos asin B C (d) ( b c)sin a cos 5. Three circular coins each of radii cm are kept in an equilateral triangle so that all the three coins touch each other and also the sides of the triangle. rea of the triangle is (a) (4 ) cm (c) (48 7 ) cm 4 ( 7 ) cm 4 (d) (6 4 ) cm 7. In a triangle BC, let C /. If r is the in-radius and is the circum-radius of the triangle then (r + ) is equal to : (a) a + b (c) c + a b + c (d) a + b + c 8. In a triangle BC, B / and C / 4. Let D divides BC internally in the ratio : then sin BD sin CD equal to : (a) / 6 / (c) / (d) / 9. If B, C a units, then 4 area (in sq. units) of traingle BC is : and (a) 6 4 (c) (d) 4 0. Let r, be respectively the radii of the inscribed and circumscribed circles of a regular polygon of n sides such that r 5, then n is equal to : (a) 5 6 (c) 0 (d) 8 r r. In a triangle BC, is equal to : bc ca ab (a) r r r (c) r (d) r [ ] Mathematics for JEE-0

2 Solution of Triangle a b c. If for a triangle BC, b c a 0 then c a b sin sin B sin C is equal to : (a) sin + sinb + sinc sin sinb sinc (c) sin + sin B + sin C (d) sin sin B sin C a b c. In a triangle BC if, then ratio of the radius of the circumcircle to that of the incircle is (a) 5/4 /5 (c) 6/7 (d) 6/ 4. In a triangle BC let D be the altitude form. If b > c, equal to o abc C and D b c (a) º º (c) 47º (d) 57º 5. In triangle BC, if cos cos B cosc a b, then a b c bc ca (a) = 90º B = 90º (c) C = 90º (d) C = 75º then B is 8. If D is the mid-point of side BC of a triangle BC and D is perpendicular to C, then (a) b = a c a = b c (c) b = a c (d) a + b = 5c 9. If two sides of a triangle are the roots of the equation 4x ( 6) x 0 and the included angle is 60º, then the third side is (a) / (c) / (d) / 0. In a triangle BC, if (a + b + c) (b + c a) = bc, then : (a) 0 6 (c) 0 4 (d) 4. Internal bisector of angle of triangle BC meets side BC at D. line drawn through D perpendicular to D intersects the side C at E and the side B at F. If a, b, c represent sides of (a) E is H.M. of b and c bc D cos b c 4bc (c) EF sin b c (d) the triangle EF is isosceles BC, then. If a triangle BC with side a = units is inscribed in a circle of radius 0 units, then in-radius of triangle BC can be : (a) 4 units (c) 5 units 8 units (d) units 6. In a triangle BC, if then C is equal to : (a) 0º 60º (c) 75º (d) 90º a c b c a b c 7. In a triangle with one angle, the lengths of the sides form an.p. If the length of the greatest side is 7 cm, the radius of the circumcircle of the triangle is (a) 7 cm (c) cm 5 cm (d) cm. Let the two adjacent sides of a cyclic quadrilateral be, 5 and the angle between them is. If the area of quadrilateral is 4 square units, then the remaining sides can be : (a) 4 (c) (d) 6 4. Which of the following expressions on solving reduce to the area of triangle BC? (all the notations are having their usual meaning). (a) r( r r r ) r r 4 ( r r ) r r (c) r r r cot r (sin ) (d) r r c b [ 4 ] Mathematics for JEE-0

3 5. For triangle BC, which of the following statements are true? (a) Product of all the side lengths of BC ( r s ). r r r r (c) If r r, then BC is right-angled. (d) If r, then BC is equilateral. 7. In triangle BC, let the side lengths be a = 6, b = 8 and c = 0. Statement : Distance between the circum-centre and in-centre of BC is equal to 5 units Statement : For any triangle, distance between the circum-centre and in-centre is equal to r, where, r represents the circum-radius and in-radius of the triangle. Following questions are assertion and reasoning type questions. Each of these questions contains two statements, Statement (ssertion) and Statement (eason). Each of these questions has four alternative answers, only one of them is the correct answer. Select the correct answer from the given options : (a) Both Statement and Statement are true and Statement is the correct explanation of Statement. Both Statement and Statement are true but Statement is not the correct explanation of Statement. (c) Statement is true but Statement is false. (d) Statement is false but Statement is true. 6. Let be the area of n-sided regular polygon inscribed in a circle 'C' of unit radius and be the area of n-sided regular polygon circumscribing the circle 'C'. Statement : If 4( ), then the number of sides ' n' of the regular polygon are Statement : 4 tan n. 8. Consider an acute-angled triangle BC in which the altitudes are P, BQ and C. Statement : Incentre of triangle PQ is the orthocentre of triangle BC Statement : orthocentre of triangle I I I is the in-centre of triangle BC, where I, I, I denote the centre of escribed circles for triangle BC. 9. Consider a triangle BC, having side lengths a, b, c and circum-radius (). If r, r, r denote the ex-radii of triangle BC, then ab ac bc Statement : 6 r r r a b b c c a Statement : 6 b a c b a c 00. Statement : In triangle BC, if the sides b, c and the angle BC is known, then a unique triangle can b only be formed if sin B and B is acute c b Statement : If sin B and B is obtuse, then c BC doesn't exist. [ 5 ] Mathematics for JEE-0

4 Solution of Triangle 6. If BC = 4 units and the area of BC is ' ' square units, then : Comprehension passage () ( Questions No. - ) (a) 4 tan sin Let circum-radius of BC be '' and the line joining the circum-centre 'O' and in-centre 'I' is parallel to side BC. If,, are the radii of circumcircles of triangles OBC, OC and OB respectively, then answer the following questions. a b c. Value of is equal to : (a) a b c (c) abc. Value of ( cosb + cosc ) is : a bc (d) (a) / (c) / (d) / a b c. For given BC the in-radius is given by : (a) cos B (c) cos C cos (d) none of these Comprehension passage () ( Questions No. 4-6 ) In triangle BC, let the altitude, internal angular bisector and the median from vertex meet the opposite side BC at D, E and F respectively. If BD, and DE EF CF, then answer the following questions. (c) tan tan cot tan (d) tan tan ( ) = Comprehension passage () ( Questions No. 7-9 ) Let triangle BC of area square units be inscribed in a circle of radius 4 units, where 0,. If p, p and p denote the length of altitudes of triangle BC from the vertices, B and C respectively, then answer the following questions. 7. The value of cos cos B cosc 4, is equal to : p p p (a) (c) (d) 4 8. If sides a, b, c are in.p., then maximum value of is equal to : p p p (a) 8 (c) 6 4 (d) 4. If { p } denotes the fractional part of p, where p = [ p ] + { p }, then : (a) {tan B} 0 {sin } = / (c) {cos B} (d) {tan B} {tan C} 9. Minimum value of the expression a p b p c p is equal to : b c a (a) 4 6 (c) 8 (d) 5. Value of tan cos (cos( C)) is equal to : B (a) tan (c) sin (B) tan 4 (d) tan B + tan C 0. Let a, b, c represent the sides of triangle BC, where (b a) = (c b) = and a, b, c N. If C, then value of (c b a) is equal to... [ 6 ] Mathematics for JEE-0

5 . If sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the largest side of triangle is.... Let a, b and c represent the sides of triangle BC opposite to the vertices, B and C respectively. If a b c b c a ( b c ) 0, then value of sec () is equal to.... Let three circles touch one-another externally and the tangents at their points of contact meet at a point whose distance from any point of contact is units. If ratio of the product of radii to the sum of radii of cricles is k :, then k is equal to If 0 is the area of formed by joining the points of contact of incircle with the sides of the given triangle whose area is, similarly, and are the corresponding area of the formed by joining the points of contact of excircles with the sides, then value of 0 is equal to In triangle BC, let the orthocentre (H) and circum-centre (C 0 ) be (, ) and (4, ) respectively. If side BC of the triangle lies on line y = 0 and internal angles are, B, C, then match the following columns (I) and (II). Column (I) Column (II) (a) ( C0) cos (p) sec HB (q) (c) H (r) 4 (d) HC (s) sec 6. In triangle BC, let CH and CM be the lengths of the altitude and median to base B. If side lengths (t) a 5, b 97 and c =, then match the following columns I and II. Column (I) Column (II) (a) Value of cos(tan ( MH )) is (p) Length of in-radius of triangle MHC is (q) (c) If BC is extended to P such that triangle PB is right angled at P, and area of PC is ' ' square units, (r) 5 then integer(s) less than can be (s) MH (d) If PH, then value of tan is more than (t) / [ 7 ] Mathematics for JEE-0

6 Solution of Triangle. (c).. (c) (d) Ex 6. (c) 7. (a) 8. (a) 9. (a) 0. (a). (d).. (c) 4. (a) 5. (a) (a) 8. (a) (c). (a, b, c, d). (a, d). (a, c) 4. (a, b, c, d) 5. (b, c, d) 6. (c) 7. (a) (a) 0. (d) E.. (a). 4. (d) 5. Ex (d) ( 9 ). ( 6 ). ( 4 ). ( 4 ) 4. ( ) 5. (a) t 6. (a) t p q (c) q (c) p, q, s (d) s (d) p, q, t [ 8 ] Mathematics for JEE-0

Q.1 If a, b, c are distinct positive real in H.P., then the value of the expression, (A) 1 (B) 2 (C) 3 (D) 4. (A) 2 (B) 5/2 (C) 3 (D) none of these

Q.1 If a, b, c are distinct positive real in H.P., then the value of the expression, (A) 1 (B) 2 (C) 3 (D) 4. (A) 2 (B) 5/2 (C) 3 (D) none of these Q. If a, b, c are distinct positive real in H.P., then the value of the expression, b a b c + is equal to b a b c () (C) (D) 4 Q. In a triangle BC, (b + c) = a bc where is the circumradius of the triangle.

More information

VKR Classes TIME BOUND TESTS 1-7 Target JEE ADVANCED For Class XI VKR Classes, C , Indra Vihar, Kota. Mob. No

VKR Classes TIME BOUND TESTS 1-7 Target JEE ADVANCED For Class XI VKR Classes, C , Indra Vihar, Kota. Mob. No VKR Classes TIME BOUND TESTS -7 Target JEE ADVANCED For Class XI VKR Classes, C-9-0, Indra Vihar, Kota. Mob. No. 9890605 Single Choice Question : PRACTICE TEST-. The smallest integer greater than log +

More information

Objective Mathematics

Objective Mathematics . A tangent to the ellipse is intersected by a b the tangents at the etremities of the major ais at 'P' and 'Q' circle on PQ as diameter always passes through : (a) one fied point two fied points (c) four

More information

QUESTION BANK ON STRAIGHT LINE AND CIRCLE

QUESTION BANK ON STRAIGHT LINE AND CIRCLE QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,

More information

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5

More information

Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40

Maharashtra Board Class X Mathematics - Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40 Maharashtra Board Class X Mathematics - Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note: - () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas

More information

[STRAIGHT OBJECTIVE TYPE] Q.4 The expression cot 9 + cot 27 + cot 63 + cot 81 is equal to (A) 16 (B) 64 (C) 80 (D) none of these

[STRAIGHT OBJECTIVE TYPE] Q.4 The expression cot 9 + cot 27 + cot 63 + cot 81 is equal to (A) 16 (B) 64 (C) 80 (D) none of these Q. Given a + a + cosec [STRAIGHT OBJECTIVE TYPE] F HG ( a x) I K J = 0 then, which of the following holds good? (A) a = ; x I a = ; x I a R ; x a, x are finite but not possible to find Q. The minimum value

More information

So, eqn. to the bisector containing (-1, 4) is = x + 27y = 0

So, eqn. to the bisector containing (-1, 4) is = x + 27y = 0 Q.No. The bisector of the acute angle between the lines x - 4y + 7 = 0 and x + 5y - = 0, is: Option x + y - 9 = 0 Option x + 77y - 0 = 0 Option x - y + 9 = 0 Correct Answer L : x - 4y + 7 = 0 L :-x- 5y

More information

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in

Chapter (Circle) * Circle - circle is locus of such points which are at equidistant from a fixed point in Chapter - 10 (Circle) Key Concept * Circle - circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle - Circle having same centre called concentric circle.

More information

[STRAIGHT OBJECTIVE TYPE] log 4 2 x 4 log. x x log 2 x 1

[STRAIGHT OBJECTIVE TYPE] log 4 2 x 4 log. x x log 2 x 1 [STRAIGHT OBJECTIVE TYPE] Q. The equation, log (x ) + log x. log x x log x + log x log + log / x (A) exactly one real solution (B) two real solutions (C) real solutions (D) no solution. = has : Q. The

More information

Chapter-wise questions

Chapter-wise questions hapter-wise questions ircles 1. In the given figure, is circumscribing a circle. ind the length of. 3 15cm 5 2. In the given figure, is the center and. ind the radius of the circle if = 18 cm and = 3cm

More information

Problems First day. 8 grade. Problems First day. 8 grade

Problems First day. 8 grade. Problems First day. 8 grade First day. 8 grade 8.1. Let ABCD be a cyclic quadrilateral with AB = = BC and AD = CD. ApointM lies on the minor arc CD of its circumcircle. The lines BM and CD meet at point P, thelinesam and BD meet

More information

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or

Q.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R

More information

LLT Education Services

LLT Education Services 8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the

More information

6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.

6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle. 6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has

More information

MT - w A.P. SET CODE MT - w - MATHEMATICS (71) GEOMETRY- SET - A (E) Time : 2 Hours Preliminary Model Answer Paper Max.

MT - w A.P. SET CODE MT - w - MATHEMATICS (71) GEOMETRY- SET - A (E) Time : 2 Hours Preliminary Model Answer Paper Max. .P. SET CODE.. Solve NY FIVE of the following : (i) ( BE) ( BD) ( BE) ( BD) BE D 6 9 MT - w 07 00 - MT - w - MTHEMTICS (7) GEOMETRY- (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40 [Triangles

More information

DEEPAWALI ASSIGNMENT CLASS 11 FOR TARGET IIT JEE 2012 SOLUTION

DEEPAWALI ASSIGNMENT CLASS 11 FOR TARGET IIT JEE 2012 SOLUTION DEEPAWALI ASSIGNMENT CLASS FOR TARGET IIT JEE 0 SOLUTION IMAGE OF SHRI GANESH LAXMI SARASWATI Director & H.O.D. IITJEE Mathematics SUHAG R. KARIYA (S.R.K. Sir) DOWNLOAD FREE STUDY PACKAGE, TEST SERIES

More information

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.

( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. Problems 01 - POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the mid-points of the pairs of opposite sides and the line

More information

POINT. Preface. The concept of Point is very important for the study of coordinate

POINT. Preface. The concept of Point is very important for the study of coordinate POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates

More information

Downloaded from

Downloaded from Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2 - AD 2 AD 2 - AC 2 3AC 2-4AD 2 (D) 4AD 2-3AC 2 2.Which of the following statement is true? Any two right triangles are similar

More information

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)

VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) BY:Prof. RAHUL MISHRA Class :- X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject :- Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ

More information

2013 Sharygin Geometry Olympiad

2013 Sharygin Geometry Olympiad Sharygin Geometry Olympiad 2013 First Round 1 Let ABC be an isosceles triangle with AB = BC. Point E lies on the side AB, and ED is the perpendicular from E to BC. It is known that AE = DE. Find DAC. 2

More information

INMO-2001 Problems and Solutions

INMO-2001 Problems and Solutions INMO-2001 Problems and Solutions 1. Let ABC be a triangle in which no angle is 90. For any point P in the plane of the triangle, let A 1,B 1,C 1 denote the reflections of P in the sides BC,CA,AB respectively.

More information

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM.

1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 1. In a triangle ABC altitude from C to AB is CF= 8 units and AB has length 6 units. If M and P are midpoints of AF and BC. Find the length of PM. 2. Let ABCD be a cyclic quadrilateral inscribed in a circle

More information

Circle and Cyclic Quadrilaterals. MARIUS GHERGU School of Mathematics and Statistics University College Dublin

Circle and Cyclic Quadrilaterals. MARIUS GHERGU School of Mathematics and Statistics University College Dublin Circle and Cyclic Quadrilaterals MARIUS GHERGU School of Mathematics and Statistics University College Dublin 3 Basic Facts About Circles A central angle is an angle whose vertex is at the center of the

More information

Plane geometry Circles: Problems with some Solutions

Plane geometry Circles: Problems with some Solutions The University of Western ustralia SHL F MTHMTIS & STTISTIS UW MY FR YUNG MTHMTIINS Plane geometry ircles: Problems with some Solutions 1. Prove that for any triangle, the perpendicular bisectors of the

More information

= 0 1 (3 4 ) 1 (4 4) + 1 (4 3) = = + 1 = 0 = 1 = ± 1 ]

= 0 1 (3 4 ) 1 (4 4) + 1 (4 3) = = + 1 = 0 = 1 = ± 1 ] STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. If the lines x + y + = 0 ; x + y + = 0 and x + y + = 0, where + =, are concurrent then (A) =, = (B) =, = ± (C) =, = ± (D*) = ±, = [Sol. Lines are x + y + = 0

More information

Chapter 1. Some Basic Theorems. 1.1 The Pythagorean Theorem

Chapter 1. Some Basic Theorems. 1.1 The Pythagorean Theorem hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a 2 + b 2 = c 2. roof. b a a 3 2 b 2 b 4 b a b

More information

SOLUTION OF TRIANGLES

SOLUTION OF TRIANGLES SOLUTION OF TIANGLES DPP by VK Sir B.TEH., IIT DELHI VK lsses, -9-40, Indr Vihr, Kot. Mob. No. 989060 . If cos A + cosb + cos = then the sides of the AB re in A.P. G.P H.P. none. If in tringle sin A :

More information

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)

10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2) 10. Circles Q 1 True or False: It is possible to draw two circles passing through three given non-collinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular

More information

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : , MCN COMPLEX NUMBER C The complex number Complex number is denoted by ie = a + ib, where a is called as real part of (denoted by Re and b is called as imaginary part of (denoted by Im Here i =, also i =,

More information

Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z.

Triangles. 3.In the following fig. AB = AC and BD = DC, then ADC = (A) 60 (B) 120 (C) 90 (D) none 4.In the Fig. given below, find Z. Triangles 1.Two sides of a triangle are 7 cm and 10 cm. Which of the following length can be the length of the third side? (A) 19 cm. (B) 17 cm. (C) 23 cm. of these. 2.Can 80, 75 and 20 form a triangle?

More information

BOARD ANSWER PAPER :OCTOBER 2014

BOARD ANSWER PAPER :OCTOBER 2014 BRD NSWER PPER :CTBER 04 GEETRY. Solve any five sub-questions: BE i. BE ( BD) D BE 6 ( BD) 9 ΔBE (ΔBD) ----[Ratio of areas of two triangles having equal base is equal to the ratio of their corresponding

More information

SSC CGL Tier 1 and Tier 2 Program

SSC CGL Tier 1 and Tier 2 Program Gurudwara Road Model Town, Hisar 9729327755 www.ssccglpinnacle.com SSC CGL Tier 1 and Tier 2 Program -------------------------------------------------------------------------------------------------------------------

More information

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths

Topic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is

More information

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola) QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents

More information

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad

TARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad J-Mathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =

More information

MATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately.

MATHEMATICS. (Two hours and a half) Answers to this Paper must be written on the paper provided separately. CLASS IX MATHEMATICS (Two hours and a half) Answers to this Paper must be written on the paper provided separately. You will not be allowed to write during the first 15 minutes. This time is to be spent

More information

1 / 23

1 / 23 CBSE-XII-07 EXAMINATION CBSE-X-009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper

More information

MAHESH TUTORIALS. Time : 1 hr. 15 min. Q.1. Solve the following : 3

MAHESH TUTORIALS. Time : 1 hr. 15 min. Q.1. Solve the following : 3 S.S.. MHESH TUTRILS Test - II atch : S Marks : 30 Date : GEMETRY hapter : 1,, 3 Time : 1 hr. 15 min..1. Solve the following : 3 The areas of two similar triangles are 18 cm and 3 cm respectively. What

More information

chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?

chapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true? chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "

More information

Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR.

Triangles. Example: In the given figure, S and T are points on PQ and PR respectively of PQR such that ST QR. Determine the length of PR. Triangles Two geometric figures having the same shape and size are said to be congruent figures. Two geometric figures having the same shape, but not necessarily the same size, are called similar figures.

More information

Integrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words.

Integrated Math II. IM2.1.2 Interpret given situations as functions in graphs, formulas, and words. Standard 1: Algebra and Functions Students graph linear inequalities in two variables and quadratics. They model data with linear equations. IM2.1.1 Graph a linear inequality in two variables. IM2.1.2

More information

MockTime.com. NDA Mathematics Practice Set 1.

MockTime.com. NDA Mathematics Practice Set 1. 346 NDA Mathematics Practice Set 1. Let A = { 1, 2, 5, 8}, B = {0, 1, 3, 6, 7} and R be the relation is one less than from A to B, then how many elements will R contain? 2 3 5 9 7. 1 only 2 only 1 and

More information

Regd. Office : Aakash Tower, Plot No.-4, Sec-11, MLU, Dwarka, New Delhi Ph.: Fax :

Regd. Office : Aakash Tower, Plot No.-4, Sec-11, MLU, Dwarka, New Delhi Ph.: Fax : Regd. Office : akash Tower, Plot No.-, Sec-, MLU, Dwarka, New Delhi-007 Ph.: 0-766 Fax : 0-767 dmission-cum-scholarship Test (Sample Paper) First Step Course for JEE (Main & dvanced) 0-07 (Syllabus of

More information

Indicate whether the statement is true or false.

Indicate whether the statement is true or false. PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.

More information

1966 IMO Shortlist. IMO Shortlist 1966

1966 IMO Shortlist. IMO Shortlist 1966 IMO Shortlist 1966 1 Given n > 3 points in the plane such that no three of the points are collinear. Does there exist a circle passing through (at least) 3 of the given points and not containing any other

More information

11 th Philippine Mathematical Olympiad Questions, Answers, and Hints

11 th Philippine Mathematical Olympiad Questions, Answers, and Hints view.php3 (JPEG Image, 840x888 pixels) - Scaled (71%) https://mail.ateneo.net/horde/imp/view.php3?mailbox=inbox&inde... 1 of 1 11/5/2008 5:02 PM 11 th Philippine Mathematical Olympiad Questions, Answers,

More information

Classical Theorems in Plane Geometry 1

Classical Theorems in Plane Geometry 1 BERKELEY MATH CIRCLE 1999 2000 Classical Theorems in Plane Geometry 1 Zvezdelina Stankova-Frenkel UC Berkeley and Mills College Note: All objects in this handout are planar - i.e. they lie in the usual

More information

Objective Mathematics

Objective Mathematics Multiple choice questions with ONE correct answer : ( Questions No. 1-5 ) 1. If the equation x n = (x + ) is having exactly three distinct real solutions, then exhaustive set of values of 'n' is given

More information

Geometry. Class Examples (July 8) Paul Yiu. Department of Mathematics Florida Atlantic University. Summer 2014

Geometry. Class Examples (July 8) Paul Yiu. Department of Mathematics Florida Atlantic University. Summer 2014 Geometry lass Examples (July 8) Paul Yiu Department of Mathematics Florida tlantic University c b a Summer 2014 1 The incircle The internal angle bisectors of a triangle are concurrent at the incenter

More information

BOARD QUESTION PAPER : MARCH 2016 GEOMETRY

BOARD QUESTION PAPER : MARCH 2016 GEOMETRY BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential

More information

CONCURRENT LINES- PROPERTIES RELATED TO A TRIANGLE THEOREM The medians of a triangle are concurrent. Proof: Let A(x 1, y 1 ), B(x, y ), C(x 3, y 3 ) be the vertices of the triangle A(x 1, y 1 ) F E B(x,

More information

Circles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle.

Circles. II. Radius - a segment with one endpoint the center of a circle and the other endpoint on the circle. Circles Circles and Basic Terminology I. Circle - the set of all points in a plane that are a given distance from a given point (called the center) in the plane. Circles are named by their center. II.

More information

2005 Palm Harbor February Invitational Geometry Answer Key

2005 Palm Harbor February Invitational Geometry Answer Key 005 Palm Harbor February Invitational Geometry Answer Key Individual 1. B. D. C. D 5. C 6. D 7. B 8. B 9. A 10. E 11. D 1. C 1. D 1. C 15. B 16. B 17. E 18. D 19. C 0. C 1. D. C. C. A 5. C 6. C 7. A 8.

More information

XIII GEOMETRICAL OLYMPIAD IN HONOUR OF I.F.SHARYGIN The correspondence round. Solutions

XIII GEOMETRICAL OLYMPIAD IN HONOUR OF I.F.SHARYGIN The correspondence round. Solutions XIII GEOMETRIL OLYMPID IN HONOUR OF I.F.SHRYGIN The correspondence round. Solutions 1. (.Zaslavsky) (8) Mark on a cellular paper four nodes forming a convex quadrilateral with the sidelengths equal to

More information

NEW YORK CITY INTERSCHOLASTIC MATHEMATICS LEAGUE Senior A Division CONTEST NUMBER 1

NEW YORK CITY INTERSCHOLASTIC MATHEMATICS LEAGUE Senior A Division CONTEST NUMBER 1 Senior A Division CONTEST NUMBER 1 PART I FALL 2011 CONTEST 1 TIME: 10 MINUTES F11A1 Larry selects a 13-digit number while David selects a 10-digit number. Let be the number of digits in the product of

More information

Geometry. A. Right Triangle. Legs of a right triangle : a, b. Hypotenuse : c. Altitude : h. Medians : m a, m b, m c. Angles :,

Geometry. A. Right Triangle. Legs of a right triangle : a, b. Hypotenuse : c. Altitude : h. Medians : m a, m b, m c. Angles :, Geometry A. Right Triangle Legs of a right triangle : a, b Hypotenuse : c Altitude : h Medians : m a, m b, m c Angles :, Radius of circumscribed circle : R Radius of inscribed circle : r Area : S 1. +

More information

PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians.

PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared by IITians. www. Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) ALP ADVANCED LEVEL PROBLEMS Straight Lines 60 Best JEE Main and Advanced Level Problems (IIT-JEE). Prepared b IITians.

More information

Geometry Honors Review for Midterm Exam

Geometry Honors Review for Midterm Exam Geometry Honors Review for Midterm Exam Format of Midterm Exam: Scantron Sheet: Always/Sometimes/Never and Multiple Choice 40 Questions @ 1 point each = 40 pts. Free Response: Show all work and write answers

More information

Theorem 1.2 (Converse of Pythagoras theorem). If the lengths of the sides of ABC satisfy a 2 + b 2 = c 2, then the triangle has a right angle at C.

Theorem 1.2 (Converse of Pythagoras theorem). If the lengths of the sides of ABC satisfy a 2 + b 2 = c 2, then the triangle has a right angle at C. hapter 1 Some asic Theorems 1.1 The ythagorean Theorem Theorem 1.1 (ythagoras). The lengths a b < c of the sides of a right triangle satisfy the relation a + b = c. roof. b a a 3 b b 4 b a b 4 1 a a 3

More information

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 4

MT - GEOMETRY - SEMI PRELIM - I : PAPER - 4 07 00 MT A.. Attempt ANY FIVE of the following : (i) Slope of the line (m) 4 y intercept of the line (c) 0 By slope intercept form, The equation of the line is y m + c y (4) + (0) y 4 MT - GEOMETRY - SEMI

More information

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.

21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then

More information

MOCKTIME.COM ONLINE TEST SERIES CORRESPONDENCE COURSE

MOCKTIME.COM ONLINE TEST SERIES CORRESPONDENCE COURSE GEOMETRY TRIANGLES AND THEIR PROPERTIES A triangle is a figure enclosed by three sides. In the figure given below, ABC is a triangle with sides AB, BC, and CA measuring c, a, and b units, respectively.

More information

2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB.

2. In ABC, the measure of angle B is twice the measure of angle A. Angle C measures three times the measure of angle A. If AC = 26, find AB. 2009 FGCU Mathematics Competition. Geometry Individual Test 1. You want to prove that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex. Which postulate/theorem

More information

Vectors - Applications to Problem Solving

Vectors - Applications to Problem Solving BERKELEY MATH CIRCLE 00-003 Vectors - Applications to Problem Solving Zvezdelina Stankova Mills College& UC Berkeley 1. Well-known Facts (1) Let A 1 and B 1 be the midpoints of the sides BC and AC of ABC.

More information

Singapore International Mathematical Olympiad Training Problems

Singapore International Mathematical Olympiad Training Problems Singapore International athematical Olympiad Training Problems 18 January 2003 1 Let be a point on the segment Squares D and EF are erected on the same side of with F lying on The circumcircles of D and

More information

INVERSION IN THE PLANE BERKELEY MATH CIRCLE

INVERSION IN THE PLANE BERKELEY MATH CIRCLE INVERSION IN THE PLANE BERKELEY MATH CIRCLE ZVEZDELINA STANKOVA MILLS COLLEGE/UC BERKELEY SEPTEMBER 26TH 2004 Contents 1. Definition of Inversion in the Plane 1 Properties of Inversion 2 Problems 2 2.

More information

Solutions to RSPL/1. Mathematics 10

Solutions to RSPL/1. Mathematics 10 Solutions to RSPL/. It is given that 3 is a zero of f(x) x 3x + p. \ (x 3) is a factor of f(x). So, (3) 3(3) + p 0 8 9 + p 0 p 9 Thus, the polynomial is x 3x 9. Now, x 3x 9 x 6x + 3x 9 x(x 3) + 3(x 3)

More information

y mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent

y mx 25m 25 4 circle. Then the perpendicular distance of tangent from the centre (0, 0) is the radius. Since tangent Mathematics. The sides AB, BC and CA of ABC have, 4 and 5 interior points respectively on them as shown in the figure. The number of triangles that can be formed using these interior points is () 80 ()

More information

Time : 2 Hours Preliminary Model Answer Paper Max. Marks : 40. [Given] [Taking square roots]

Time : 2 Hours Preliminary Model Answer Paper Max. Marks : 40. [Given] [Taking square roots] .P. SET CODE MT - w 05 00 - MT - w - MTHEMTICS (7) GEOMETRY - (E) Time : Hours Preliminary Model nswer Paper Max. Marks : 40.. ttempt NY FIVE of the following : (i) BC ~ PQ [Given] ( BC) ( PQ) BC PQ [reas

More information

1 / 23

1 / 23 CBSE-XII-017 EXAMINATION CBSE-X-008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question

More information

UNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction

UNIT 3 CIRCLES AND VOLUME Lesson 1: Introducing Circles Instruction Prerequisite Skills This lesson requires the use of the following skills: performing operations with fractions understanding slope, both algebraically and graphically understanding the relationship of

More information

Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1

Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1 Calgary Math Circles: Triangles, Concurrency and Quadrilaterals 1 1 Triangles: Basics This section will cover all the basic properties you need to know about triangles and the important points of a triangle.

More information

Secondary School Certificate Examination Syllabus MATHEMATICS. Class X examination in 2011 and onwards. SSC Part-II (Class X)

Secondary School Certificate Examination Syllabus MATHEMATICS. Class X examination in 2011 and onwards. SSC Part-II (Class X) Secondary School Certificate Examination Syllabus MATHEMATICS Class X examination in 2011 and onwards SSC Part-II (Class X) 15. Algebraic Manipulation: 15.1.1 Find highest common factor (H.C.F) and least

More information

CLASS IX GEOMETRY MOCK TEST PAPER

CLASS IX GEOMETRY MOCK TEST PAPER Total time:3hrs darsha vidyalay hunashyal P. M.M=80 STION- 10 1=10 1) Name the point in a triangle that touches all sides of given triangle. Write its symbol of representation. 2) Where is thocenter of

More information

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions

Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,

More information

Homework Assignments Math /02 Fall 2017

Homework Assignments Math /02 Fall 2017 Homework Assignments Math 119-01/02 Fall 2017 Assignment 1 Due date : Wednesday, August 30 Section 6.1, Page 178: #1, 2, 3, 4, 5, 6. Section 6.2, Page 185: #1, 2, 3, 5, 6, 8, 10-14, 16, 17, 18, 20, 22,

More information

( Bifurcated Syllabus ) ( According to Syllabus of Class X only) PART - I

( Bifurcated Syllabus ) ( According to Syllabus of Class X only) PART - I Karunamoyee, Salt Lake, Kolkata : 70009 Mathematics (COMPULSORY) (Compulsory) Full marks : NEW 90 - For SYLLABUS Regular Candidates { Time 00 ---3 Hours - For 5 Eternal Minutes Candidates ( First 5 minutes

More information

Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =

Question 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain = Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain

More information

Circles. Exercise 9.1

Circles. Exercise 9.1 9 uestion. Exercise 9. How many tangents can a circle have? Solution For every point of a circle, we can draw a tangent. Therefore, infinite tangents can be drawn. uestion. Fill in the blanks. (i) tangent

More information

STRAIGHT LINES EXERCISE - 3

STRAIGHT LINES EXERCISE - 3 STRAIGHT LINES EXERCISE - 3 Q. D C (3,4) E A(, ) Mid point of A, C is B 3 E, Point D rotation of point C(3, 4) by angle 90 o about E. 3 o 3 3 i4 cis90 i 5i 3 i i 5 i 5 D, point E mid point of B & D. So

More information

Chapter 4. Feuerbach s Theorem

Chapter 4. Feuerbach s Theorem Chapter 4. Feuerbach s Theorem Let A be a point in the plane and k a positive number. Then in the previous chapter we proved that the inversion mapping with centre A and radius k is the mapping Inv : P\{A}

More information

Trans Web Educational Services Pvt. Ltd B 147,1st Floor, Sec-6, NOIDA, UP

Trans Web Educational Services Pvt. Ltd B 147,1st Floor, Sec-6, NOIDA, UP Solved Examples Example 1: Find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4, x + 2y = 5. Method 1. Consider the equation (x + y 6) (2x + y 4) + λ 1

More information

DESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80

DESIGN OF THE QUESTION PAPER Mathematics Class X NCERT. Time : 3 Hours Maximum Marks : 80 DESIGN OF THE QUESTION PAPER Mathematics Class X Weightage and the distribution of marks over different dimensions of the question shall be as follows: (A) Weightage to Content/ Subject Units : S.No. Content

More information

HEAT-3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAX-MARKS-(112(3)+20(5)=436)

HEAT-3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAX-MARKS-(112(3)+20(5)=436) HEAT- APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA TIME-(HRS) Select the correct alternative : (Only one is correct) MAX-MARKS-(()+0(5)=6) Q. Suppose & are the point of maimum and the point of minimum

More information

MODEL QUESTION PAPERS WITH ANSWERS SET 1

MODEL QUESTION PAPERS WITH ANSWERS SET 1 MTHEMTICS MODEL QUESTION PPERS WITH NSWERS SET 1 Finish Line & Beyond CLSS X Time llowed: 3 Hrs Max. Marks : 80 General Instructions: (1) ll questions are compulsory. (2) The question paper consists of

More information

[Class-X] MATHEMATICS SESSION:

[Class-X] MATHEMATICS SESSION: [Class-X] MTHEMTICS SESSION:017-18 Time allowed: 3 hrs. Maximum Marks : 80 General Instructions : (i) ll questions are compulsory. (ii) This question paper consists of 30 questions divided into four sections,

More information

CAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date :

CAREER POINT PRE FOUNDATION DIVISON CLASS-9. IMO Stage-II Exam MATHEMATICS Date : CAREER POINT PRE FOUNDATION DIVISON IMO Stage-II Exam.-07 CLASS-9 MATHEMATICS Date : -0-07 Q. In the given figure, PQR is a right angled triangle, right angled at Q. If QRST is a square on side QR and

More information

(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F)

(A) 50 (B) 40 (C) 90 (D) 75. Circles. Circles <1M> 1.It is possible to draw a circle which passes through three collinear points (T/F) Circles 1.It is possible to draw a circle which passes through three collinear points (T/F) 2.The perpendicular bisector of two chords intersect at centre of circle (T/F) 3.If two arcs of a circle

More information

Solved Paper SSC Maharashtra Exam March 207 Class - X Geometry Time : 2 Hours Max. Marks : 40 Note : (i) Solve all questions. Draw diagrams wherever necessary. (ii) Use of calculator is not allowed. (iii)

More information

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch

Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1-Complete 1. in the parallelogram, each two opposite

More information

The circumcircle and the incircle

The circumcircle and the incircle hapter 4 The circumcircle and the incircle 4.1 The Euler line 4.1.1 nferior and superior triangles G F E G D The inferior triangle of is the triangle DEF whose vertices are the midpoints of the sides,,.

More information

CBSE X Mathematics 2012 Solution (SET 1) Section B

CBSE X Mathematics 2012 Solution (SET 1) Section B CBSE X Mathematics 01 Solution (SET 1) Section B Q11. Find the value(s) of k so that the quadratic equation x kx + k = 0 has equal roots. Given equation is x kx k 0 For the given equation to have equal

More information

Homework Assignments Math /02 Fall 2014

Homework Assignments Math /02 Fall 2014 Homework Assignments Math 119-01/02 Fall 2014 Assignment 1 Due date : Friday, September 5 6th Edition Problem Set Section 6.1, Page 178: #1, 2, 3, 4, 5, 6. Section 6.2, Page 185: #1, 2, 3, 5, 6, 8, 10-14,

More information

Chapter 4 Trigonometric Functions

Chapter 4 Trigonometric Functions SECTION 4.1 Special Right Triangles and Trigonometric Ratios Chapter 4 Trigonometric Functions Section 4.1: Special Right Triangles and Trigonometric Ratios Special Right Triangles Trigonometric Ratios

More information

CO-ORDINATE GEOMETRY. 1. Find the points on the y axis whose distances from the points (6, 7) and (4,-3) are in the. ratio 1:2.

CO-ORDINATE GEOMETRY. 1. Find the points on the y axis whose distances from the points (6, 7) and (4,-3) are in the. ratio 1:2. UNIT- CO-ORDINATE GEOMETRY Mathematics is the tool specially suited for dealing with abstract concepts of any ind and there is no limit to its power in this field.. Find the points on the y axis whose

More information

Statistics. To find the increasing cumulative frequency, we start with the first

Statistics. To find the increasing cumulative frequency, we start with the first Statistics Relative frequency = frequency total Relative frequency in% = freq total x100 To find the increasing cumulative frequency, we start with the first frequency the same, then add the frequency

More information

C=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle

C=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle 10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by

More information

SM2H Unit 6 Circle Notes

SM2H Unit 6 Circle Notes Name: Period: SM2H Unit 6 Circle Notes 6.1 Circle Vocabulary, Arc and Angle Measures Circle: All points in a plane that are the same distance from a given point, called the center of the circle. Chord:

More information