Grade 9 Circles. Answer the questions. For more such worksheets visit
|
|
- Paulina Montgomery
- 5 years ago
- Views:
Transcription
1 ID : ae-9-circles [1] Grade 9 Circles For more such worksheets visit Answer the questions (1) Two circles with centres O and O intersect at two points A and B. A line PQ is drawn parallel to OO through A(or B) intersecting the circles at P and Q. Find the ratio PQ:OO. (2) The bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing it at the points P and Q. If radius of the circle is 4 cm, find the distance between points P and Q. (3) A chord of a circle is equal to its radius. Find the angle subtended by this chord at a point in the minor segment. (4) If ACB = 25 and ABD = 40, find angle BAD. (5) ABCD is a parallelogram. The circle through A, B and C intersect CD (produced if necessary) at E. Find value of AE. AD (6) There is a circular park of radius 15 meters. Three friends Atifa, Akila and Ginton are sitting at equal distance on its boundary each having a toy telephone (connected using strings) in their hands to talk each other. Find the length of the string between a pair of the telephones.
2 ID : ae-9-circles [2] (7) The Ferris Wheel at the school fair has radius of 12 metres. It revolves at the rate of one revolution per 2 minutes. How many seconds does it take a rider to travel from the bottom of the wheel to a point 6 vertical metres above the bottom? (8) AB is diameter of the circle. If A and B are connected to E, circle is intersected at C and D respectively. If AB = 18 cm and CD = 9 cm, find AEB. (9) If ADC = 125 and chord BC = chord BE. Find CBE. (10) Two chords AB and AC of a circle subtends angles equal to 50 and 30, respectively at the centre. Find BAC, if AB and AC lie on the opposite sides of the centre. (11) If BC is a diameter of the circle and BAO = 30. Then find the value of ADC. (12) AB and AC are two chords of a circle such that AB = 2AC. If distances of AB and AC from the centre are 3 cm and 4 cm respectively, find the area of circle. (Assume π =3) (13) Two circles with radii of 9 and 14 are drawn with the same center. The smaller inner circle is painted red, and the part outside the smaller circle and inside the larger circle is painted green. What is the ratio of the areas painted green to the area painted red?
3 ID : ae-9-circles [3] Check True/False (14) Two congruent circles with centres O and O intersect at two points A and B. Then, AOB = AO'B. True False (15) If two arcs of a circle are congruent, then their corresponding chords are equal. True False 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at
4 Answers ID : ae-9-circles [4] (1) 2:1 Consider the image below: We see that the line drawn at point O perpendicular to OO meets the line PQ at a point R. A similar line drawn at O meets PQ at a point S. Now, PA is a chord, and OR is a line perpendicular to it drawn from the centre of the circle. We know that a perpendicular drawn from the centre of a circle to a chord bisects the chord. Therefore, OR bisects PA, i.e. PR = RA or PA = 2RA. Similarly, AQ = 2AS. We know, PQ = PA + AQ PQ = 2RA + 2AS PQ = 2(RA + AS) PQ = 2OO (RA + AS is the same as OO ) The ratio of PQ:OO is 2:1.
5 (2) 8 cm ID : ae-9-circles [5] Look at the image below: We consider the cyclic quadrilateral ABCD. Bisecting the angle DAB, we get the bisector which intersects the circle at P. Bisecting the opposite angle DCB, we get the bisector intersecting the circle at Q. Given the radius of the circle, we need to find the length of the segment PQ. Since, ABCD is a cyclic quadrilateral, DAB + BCD = ( DAB + BCD) = 90 2 PAD + QCD = 90 (Since AP bisects DAB and QC bisects BCD.) Now, we see that QCD = QAD (Angles subtended by the same segment, QD in this case, to points on the circumference are equal.) Using the equation obtained in step 2. We have, PAD + QAD = 90 PAQ= 90 This means that PAQ is the angle in a semi-circle. PQ is the diameter of the circle. As, PQ is the diameter of the circle, it is twice the radius. PQ = 2 4 cm = 8 cm
6 (3) 150 ID : ae-9-circles [6] Look at the image below: The chord AB has a length equal to the radius of the circle. This means that ΔOAB is an equilateral triangle. (all the sides and angels are equal and each angle measure 60 ) So, AOB = 60. We know that the angle subtended by a chord at the center is twice the angle subtended by the chord at a point in the major segment. Consider a point R on the major segment. AOB = 2 ARB. Therefore, ARB = 30 Now, consider a point S on the minor segment. ARBS is a cyclic quadrilateral, and the opposite angles of such a quadrilateral sum up to 180. ARB + ASB = 180 ASB = ARB = = 150
7 (4) 115 ID : ae-9-circles [7] Angle ADB = ACB [ Angels inscribed by same chord AB] Angle ADB = ( BAD + ABD ) [ Angels of triangle ABD] On equating RHS of above equations ACB = ( BAD + ABD ) Now replace the values of ACB and ABD in above equations and solve for BAD BAD = 115 (5) 1 ABC = AEC Since ABC = ADE ADE = AEC [ Opposite angels of cyclic quadrilateral are supplementary.] [ Opposite angles of parallelogram are equal.] ADE = AED [ AEC = AED] Step 5 Since ADE is isosceles with angles ADE = AED, AD = AE, therefore AE AD = 1.
8 (6) 15 3 m ID : ae-9-circles [8] Take a look at the image below, which represents the scenario outlined in the question. The corners of the triangle A, B and C represent the three friends Atifa, Akila and Ginton O is the center of the cirlce ABC is an equilateral triangle, and we connect A, B and C to the center O. We can see that BOC = COA = AOB = 120 (remember, for instance BAC = 60, and the angle subtended by a chord to the center is double the angle subtended to the angle at the circumference) We also draw perpendiculars from the center to AB, CA and BC, meeting the lines at points P, Q and R respectively Take the triangle BOR (and remember that the same will hold true for triangles ROC, COQ, QOA, AOP and BOP) For triangle BOR, ORB = 90, RBO = 30, BOR = 60 (since it bisects BOC), and therefore RBO = 30 So BOR is a triangle We know that the sides of a triangle are in the proportion 1: :2 This means RO:RB:OB=1: :2 We know OB = radius = 15 m Therefore RB = Length of the string between A and B = 2 x RB = 15 3 m
9 (7) 20 seconds ID : ae-9-circles [9] After travelling 6 vertical metres from the point of start C, its new position is B. Let us consider triangle ABO and ABC: We have: AB is common AC = AO = 6 m (AC = 12-6 = 6 m) Angle BAO = Angle BAC (right angles) This means triangles ABO and ABC are congruent. From step 2 we have BC = OB = 12 m. Now we have BC = OB = CO = 12 m. This means that triangle BCO is an equilateral triangle. We know that all interior angles of an equilateral triangle are equal to 60 degrees, we have Angle COB = 60. Step 5 One revolution is equal to 360 degrees, which, according to the question, is completed in 2 minutes. 360º in 2 minutes Or, 360º in 2 60 = 120 seconds 60º in = 20 seconds. 360 Step 6 It takes rider 20 seconds to travel 6 vertical metres from the point of start. (8) 60
10 (9) 110 ID : ae-9-circles [10] ABCD is a cyclic quadrilateral since all the four points A, B, C and D lie on the circumference of a circle. We know, the opposite angles of a cyclic quadrilateral add up to 180. So, ADC + CBA = 180 CBA = ADC CBA = CBA = 55 We know that chord BC = chord BE. Join the points C and E to the centre of the circle. Consider ΔCOE and ΔBOE, BO = BO (common) BC = BE (given) OC = OE (radius of the circle) So, ΔCOE ΔBOE by the property SSS. Hence, OBC = OBE by CPCT We have, OBC = OBE = CBA = 55 Therefore, CBE = OBC + OBE = = 110.
11 (10) 140 ID : ae-9-circles [11] If we consider that the center of the circle is O, then AOB = 50 and AOC = 30 In ΔOAB, we know that BAO = ABO, (As, OB = OA and angle opposite to equal sides are equal) and BAO + ABO + AOB = 180 (Angle sum property) 2 BAO + AOB = 180 BAO = 1 2 (180 - AOB) = 1 2 ( ) = 65 Similarly, CAO = 1 2 (180 - AOC) = 1 2 ( ) = 75 Now, BAC = BAO + CAO = = 140
12 (11) 30 ID : ae-9-circles [12] As,OA and OB are the radius of the circle, OA = OB. This means ΔAOB is an isosceles triangle. So, ABO = BAO = 30. Also, ABO = ABC Considering the chord AC, ABC and ADC are the angles subtended by the chord AC in the same segment of the circle. We know that the angle subtended by a chord in the same segment of a circle are equal. So, ABC = ADC Therefore, ADC = ABC = 30. (12) 55 cm 2 Take a look at the representative image below: We are told that AB = 2AC. Also, if the perpendicular from O to AC meets the chord at Q, then OQ = 4 cm. Similarly, OP = 3 cm. As the perpendicular from the centre on the chord bisects the chord, OQ bisects AC, and OP bisects AB. From the earlier relation AB = 2AC. Therefore, BP = 2CQ
13 Let us assume CQ = x. Then, BP = 2x ID : ae-9-circles [13] Now consider ΔOQC, OC = r, the radius of the circle, and OQ = 4 cm As, the distance of a chord from the centre is always the perpendicular distance. ΔOQC is a rightangled triangle. By using pythagoras theorum, OQ 2 + CQ 2 = r x 2 = r 2 or, 16 + x 2 = r (1) Similarly, ΔOPB is a right-angled triangle, OP 2 + BP 2 = r (2x) 2 = r 2 or, 9 + 4x 2 = r (2) Step 5 Subtracting equation (1) from equation (2), we get: (9-16) + (4x 2 - x 2 ) = 0 or, 3x 2 = 7 or, x 2 = 7 3 Step 6 On substituting x 2 = 7 3 in equation (1), we get: = r 2 or, r 2 = = 55 3 Step 7 Therefore, area of the circle = πr 2 = = 55 cm 2
14 (13) 115:81 ID : ae-9-circles [14] Following figure shows the circles with radii 9 and 14 are drawn with the same center, We know that the area of a circle = π(r) 2 According to the question, the smaller inner circle is painted red, and the part outside the smaller circle and inside the larger circle is painted green. The area painted red = The area of the smaller inner circle = π(9) 2 = 81π The area painted green = The area of the larger circle - The area of the smaller inner circle = π(14) 2 - π(9) 2 = π( ) = π(196-81) = 115π Thus, the ratio of the areas painted green to the area painted red = 115π 81π = = 115:81.
15 (14) True ID : ae-9-circles [15] We are given that the circles are congruent, which means they have the same radius. We can say that OA = O'A = OB = O'B = r, where r is the radius of the circle. Now, consider ΔOAB and ΔO'AB, we have OA = O'A (Radius) OB = O'B (Radius) AB = AB (common side) Hence, ΔOAB ΔOAB by the property of SSS. As, ΔOAB ΔOAB, we can say that AOB = AO'B by CPCT. Hence, the statement is true.
16 (15) True ID : ae-9-circles [16] In the figure given below PQ and RS are the two chords that are equal, OC and OD are the perpendiculars drawn to the chords from the centre. Consider ΔPCA and ΔRDB. We know that the perpendicular to the chord from the centre bisects the chord. Since, the chords PQ and RS are equal. This means PC = RD and CQ = DS. As, we know that equal chords are equidistant from the center, OC = OD. We also know that OA = OB, as both are the radius. Subtracting the two equations, OA - OC = OB - OD AC = BD. So, in ΔPCA and ΔRDB. We have, PC = RD (From step 2) AC = BD (From step 3) PCA = RDB = 90 (By construction) Hence, ΔPCA ΔRDB by SAS So, RB = PA by CPCT Step 5 Similary, ΔDBS ΔCAQ. Hence, SB = QA by CPCT. Step 6 Now, we have RB = PA and SB = QA, on adding both we have RB + SB = PA + QA. The lengths PA + QA and RB + SB can be taken to be an approximate measure of the length of the arc PAQ and arc RBS respectively. Step 7 This means if two chords of a circle are equal, their corresponding arcs are congruent. Hence, the statement is true.
Grade 9 Circles. Answer t he quest ions. For more such worksheets visit
ID : th-9-circles [1] Grade 9 Circles For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it
More informationClass 9 Geometry-Overall
ID : in-9-geometry-overall [1] Class 9 Geometry-Overall For more such worksheets visit www.edugain.com Answer t he quest ions (1) AB is diameter of the circle. If A and B are connected to E, circle is
More informationGrade 9 Geometry-Overall
ID : au-9-geometry-overall [1] Grade 9 Geometry-Overall For more such worksheets visit www.edugain.com Answer t he quest ions (1) A chord of a circle is equal to its radius. Find the angle subtended by
More information21. 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 informationExercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior)
Exercise 10.1 Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater than its radius lies
More informationFill in the blanks Chapter 10 Circles Exercise 10.1 Question 1: (i) The centre of a circle lies in of the circle. (exterior/ interior) (ii) A point, whose distance from the centre of a circle is greater
More informationClass IX - NCERT Maths Exercise (10.1)
Class IX - NCERT Maths Exercise (10.1) Question 1: Fill in the blanks (i) The centre of a circle lies in of the circle. (exterior/interior) (ii) A point, whose distance from the centre of a circle is greater
More information10. 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(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 informationEXERCISE 10.1 EXERCISE 10.2
NCERT Class 9 Solved Questions for Chapter: Circle 10 NCERT 10 Class CIRCLES 9 Solved Questions for Chapter: Circle EXERCISE 10.1 Q.1. Fill in the blanks : (i) The centre of a circle lies in of the circle.
More information(5) Find the resultant shape obtained by connecting points (0, 5) (0, 20) (25, 20) and (25, 5).
ID : ww-9-olympiad [1] Grade 9 Olympiad For more such worksheets visit www.edugain.com Answer t he quest ions (1) If a cone and hemisphere stands on equal bases, and have the same height. Find the ratio
More informationChapter (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 informationCHAPTER 10 CIRCLES Introduction
168 MATHEMATICS CIRCLES CHAPTER 10 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of
More informationPage 1 of 15. Website: Mobile:
Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5
More informationClass 7 Lines and Angles
ID : in-7-lines-and-angles [1] Class 7 Lines and Angles For more such worksheets visit www.edugain.com Answer the questions (1) ABCD is a quadrilateral whose diagonals intersect each other at point O such
More informationProperties of the Circle
9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference
More informationSOLUTIONS SECTION A [1] = 27(27 15)(27 25)(27 14) = 27(12)(2)(13) = cm. = s(s a)(s b)(s c)
1. (A) 1 1 1 11 1 + 6 6 5 30 5 5 5 5 6 = 6 6 SOLUTIONS SECTION A. (B) Let the angles be x and 3x respectively x+3x = 180 o (sum of angles on same side of transversal is 180 o ) x=36 0 So, larger angle=3x
More informationMath 9 Chapter 8 Practice Test
Name: Class: Date: ID: A Math 9 Chapter 8 Practice Test Short Answer 1. O is the centre of this circle and point Q is a point of tangency. Determine the value of t. If necessary, give your answer to the
More informationVAISHALI 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 informationLLT 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 informationCHAPTER 7 TRIANGLES. 7.1 Introduction. 7.2 Congruence of Triangles
CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. You know that a closed figure formed by three intersecting lines is called a
More informationPLC Papers. Created For:
PLC Papers Created For: ed by use of accompanying mark schemes towards the rear to attain 8 out of 10 marks over time by completing Circle Theorems 1 Grade 8 Objective: Apply and prove the standard circle
More informationIt is known that the length of the tangents drawn from an external point to a circle is equal.
CBSE -MATHS-SET 1-2014 Q1. The first three terms of an AP are 3y-1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)
More informationQuestion 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD?
Class IX - NCERT Maths Exercise (7.1) Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? Solution 1: In ABC and ABD,
More informationTriangles. 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 informationClass IX Chapter 7 Triangles Maths. Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure).
Exercise 7.1 Question 1: In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD, AC = AD (Given) CAB = DAB (AB bisects
More information3. AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is:
Solved Paper 2 Class 9 th, Mathematics, SA 2 Time: 3hours Max. Marks 90 General Instructions 1. All questions are compulsory. 2. Draw neat labeled diagram wherever necessary to explain your answer. 3.
More informationClass IX Chapter 7 Triangles Maths
Class IX Chapter 7 Triangles Maths 1: Exercise 7.1 Question In quadrilateral ACBD, AC = AD and AB bisects A (See the given figure). Show that ABC ABD. What can you say about BC and BD? In ABC and ABD,
More informationQuestion Bank Tangent Properties of a Circle
Question Bank Tangent Properties of a Circle 1. In quadrilateral ABCD, D = 90, BC = 38 cm and DC = 5 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 7 cm. Find
More informationClass IX Chapter 8 Quadrilaterals Maths
Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Answer: Let the common ratio between
More informationClass IX Chapter 8 Quadrilaterals Maths
1 Class IX Chapter 8 Quadrilaterals Maths Exercise 8.1 Question 1: The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral. Let the common ratio between the angles
More informationCIRCLES MODULE - 3 OBJECTIVES EXPECTED BACKGROUND KNOWLEDGE. Circles. Geometry. Notes
Circles MODULE - 3 15 CIRCLES You are already familiar with geometrical figures such as a line segment, an angle, a triangle, a quadrilateral and a circle. Common examples of a circle are a wheel, a bangle,
More information= ( +1) BP AC = AP + (1+ )BP Proved UNIT-9 CIRCLES 1. Prove that the parallelogram circumscribing a circle is rhombus. Ans Given : ABCD is a parallelogram circumscribing a circle. To prove : - ABCD is
More information2012 GCSE Maths Tutor All Rights Reserved
2012 GCSE Maths Tutor All Rights Reserved www.gcsemathstutor.com This book is under copyright to GCSE Maths Tutor. However, it may be distributed freely provided it is not sold for profit. Contents angles
More informationClass 9 Quadrilaterals
ID : in-9-quadrilaterals [1] Class 9 Quadrilaterals For more such worksheets visit www.edugain.com Answer t he quest ions (1) The diameter of circumcircle of a rectangle is 13 cm and rectangle's width
More informationChapter 3 Cumulative Review Answers
Chapter 3 Cumulative Review Answers 1a. The triangle inequality is violated. 1b. The sum of the angles is not 180º. 1c. Two angles are equal, but the sides opposite those angles are not equal. 1d. The
More informationCBSE 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 informationVisit: ImperialStudy.com For More Study Materials Class IX Chapter 12 Heron s Formula Maths
Exercise 1.1 1. Find the area of a triangle whose sides are respectively 150 cm, 10 cm and 00 cm. The triangle whose sides are a = 150 cm b = 10 cm c = 00 cm The area of a triangle = s(s a)(s b)(s c) Here
More informationChapter 3. - parts of a circle.
Chapter 3 - parts of a circle. 3.1 properties of circles. - area of a sector of a circle. the area of the smaller sector can be found by the following formula: A = qº 360º pr2, given q in degrees, or!
More informationGrade 9 Lines and Angles
ID : ww-9-lines-and-angles [1] Grade 9 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If CD is perpendicular to AB, and CE bisect angle ACB, f ind the angle
More informationPRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES
PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation
More informationTRIANGLES CHAPTER 7. (A) Main Concepts and Results. (B) Multiple Choice Questions
CHAPTER 7 TRIANGLES (A) Main Concepts and Results Triangles and their parts, Congruence of triangles, Congruence and correspondence of vertices, Criteria for Congruence of triangles: (i) SAS (ii) ASA (iii)
More informationThe High School Section
1 Viète s Relations The Problems. 1. The equation 10/07/017 The High School Section Session 1 Solutions x 5 11x 4 + 4x 3 + 55x 4x + 175 = 0 has five distinct real roots x 1, x, x 3, x 4, x 5. Find: x 1
More informationAREA RELATED TO CIRCLES
CHAPTER 11 AREA RELATED TO CIRCLES (A) Main Concepts and Results Perimeters and areas of simple closed figures. Circumference and area of a circle. Area of a circular path (i.e., ring). Sector of a circle
More informationGrade 9 Lines and Angles
ID : sg-9-lines-and-angles [1] Grade 9 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If AB and PQ are parallel, compute the angle Z. (2) Find the value of a+b.
More information0811ge. Geometry Regents Exam BC, AT = 5, TB = 7, and AV = 10.
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 2) 8 3) 3 4) 6 2 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationGrade 7 Lines and Angles
ID : ph-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If CD is perpendicular to AB, and CE bisect angle ACB, f ind the angle
More informationQuestion 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 informationClass X Chapter 12 Areas Related to Circles Maths
Exercise 12.1 Question 1: The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles. Radius
More informationClass X Delhi Math Set-3 Section A
Class X Delhi Math Set-3 Section A 1. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30. The distance of the car from the base of the tower (in m.) is:
More informationMathematics 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 informationMaharashtra 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 information9 th CBSE Mega Test - II
9 th CBSE Mega Test - II Time: 3 hours Max. Marks: 90 General Instructions All questions are compulsory. The question paper consists of 34 questions divided into four sections A, B, C and D. Section A
More informationMOCKTIME.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 informationGrade 9 Quadrilaterals
ID : ww-9-quadrilaterals [1] Grade 9 Quadrilaterals For more such worksheets visit www.edugain.com Answer t he quest ions (1) ABCD is a rectangle and point P is such that PB = 3 2 cm, PC = 4 cm and PD
More informationSHW 1-01 Total: 30 marks
SHW -0 Total: 30 marks 5. 5 PQR 80 (adj. s on st. line) PQR 55 x 55 40 x 85 6. In XYZ, a 90 40 80 a 50 In PXY, b 50 34 84 M+ 7. AB = AD and BC CD AC BD (prop. of isos. ) y 90 BD = ( + ) = AB BD DA x 60
More informationGeometry: Introduction, Circle Geometry (Grade 12)
OpenStax-CNX module: m39327 1 Geometry: Introduction, Circle Geometry (Grade 12) Free High School Science Texts Project This work is produced by OpenStax-CNX and licensed under the Creative Commons Attribution
More informationClass 6 Geometry. Answer the questions. For more such worksheets visit (1) If AB and DE are parallel, find the value of ACB.
ID : in-6-geometry [1] Class 6 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) If AB and DE are parallel, find the value of ACB. (2) If AB and DE are parallel to each other,
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
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 informationMath 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper.
Math 5 Trigonometry Fair Game for Chapter 1 Test Show all work for credit. Write all responses on separate paper. 12. What angle has the same measure as its complement? How do you know? 12. What is the
More information6 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 information1 / 24
CBSE-XII-017 EXAMINATION CBSE-X-01 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instuctions : 1. All questions are compulsory.. The question paper consists of 34 questions
More informationMathematics Class X Board Paper 2011
Mathematics Class X Board Paper Solution Section - A (4 Marks) Soln.. (a). Here, p(x) = x + x kx + For (x-) to be the factor of p(x) = x + x kx + P () = Thus, () + () k() + = 8 + 8 - k + = k = Thus p(x)
More informationUdaan School Of Mathematics Class X Chapter 10 Circles Maths
Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in
More informationKENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION
KENDRIYA VIDYALAYA SANGATHAN, HYDERABAD REGION SAMPLE PAPER 01 F PERIODIC TEST III EXAM (2017-18) SUBJECT: MATHEMATICS(041) BLUE PRINT : CLASS IX Unit Chapter VSA (1 mark) SA I (2 marks) SA II (3 marks)
More informationGrade 7 Lines and Angles
ID : ae-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) If lines AC and BD intersects at point O such that AOB: BOC = 3:2, f ind
More informationLabel carefully each of the following:
Label carefully each of the following: Circle Geometry labelling activity radius arc diameter centre chord sector major segment tangent circumference minor segment Board of Studies 1 These are the terms
More information1 / 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 information0811ge. Geometry Regents Exam
0811ge 1 The statement "x is a multiple of 3, and x is an even integer" is true when x is equal to 1) 9 ) 8 3) 3 4) 6 In the diagram below, ABC XYZ. 4 Pentagon PQRST has PQ parallel to TS. After a translation
More informationGrade 7 Lines and Angles
ID : ww-7-lines-and-angles [1] Grade 7 Lines and Angles For more such worksheets visit www.edugain.com Answer t he quest ions (1) WXYZ is a quadrilateral whose diagonals intersect each other at the point
More informationCh 10 Review. Multiple Choice Identify the choice that best completes the statement or answers the question.
Ch 10 Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In the diagram shown, the measure of ADC is a. 55 b. 70 c. 90 d. 180 2. What is the measure
More informationCOMMON UNITS OF PERIMITER ARE METRE
MENSURATION BASIC CONCEPTS: 1.1 PERIMETERS AND AREAS OF PLANE FIGURES: PERIMETER AND AREA The perimeter of a plane figure is the total length of its boundary. The area of a plane figure is the amount of
More informationieducation.com Tangents given as follows. the circle. contact. There are c) Secant:
h Tangents and Secants to the Circle A Line and a circle: let us consider a circle and line say AB. There can be three possibilities given as follows. a) Non-intersecting line: The line AB and the circle
More informationchapter 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 informationSSC 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 informationRMT 2014 Geometry Test Solutions February 15, 2014
RMT 014 Geometry Test Solutions February 15, 014 1. The coordinates of three vertices of a parallelogram are A(1, 1), B(, 4), and C( 5, 1). Compute the area of the parallelogram. Answer: 18 Solution: Note
More information16 circles. what goes around...
16 circles. what goes around... 2 lesson 16 this is the first of two lessons dealing with circles. this lesson gives some basic definitions and some elementary theorems, the most important of which is
More informationBOARD 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 informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 17, 2011 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
More informationAnswer Key. 9.1 Parts of Circles. Chapter 9 Circles. CK-12 Geometry Concepts 1. Answers. 1. diameter. 2. secant. 3. chord. 4.
9.1 Parts of Circles 1. diameter 2. secant 3. chord 4. point of tangency 5. common external tangent 6. common internal tangent 7. the center 8. radius 9. chord 10. The diameter is the longest chord in
More information0809ge. Geometry Regents Exam Based on the diagram below, which statement is true?
0809ge 1 Based on the diagram below, which statement is true? 3 In the diagram of ABC below, AB AC. The measure of B is 40. 1) a b ) a c 3) b c 4) d e What is the measure of A? 1) 40 ) 50 3) 70 4) 100
More information0610ge. Geometry Regents Exam The diagram below shows a right pentagonal prism.
0610ge 1 In the diagram below of circle O, chord AB chord CD, and chord CD chord EF. 3 The diagram below shows a right pentagonal prism. Which statement must be true? 1) CE DF 2) AC DF 3) AC CE 4) EF CD
More informationMathematics CLASS : X. Time: 3hrs Max. Marks: 90. 2) If a, 2 are three consecutive terms of an A.P., then the value of a.
1 SAMPLE PAPER 4 (SAII) MR AMIT. KV NANGALBHUR Mathematics CLASS : X Time: 3hrs Max. Marks: 90 General Instruction:- 1. All questions are Compulsory. The question paper consists of 34 questions divided
More informationSOLUTIONS SECTION A SECTION B
SOLUTIONS SECTION A 1. C (1). A (1) 3. B (1) 4. B (1) 5. C (1) 6. B (1) 7. A (1) 8. D (1) SECTION B 9. 3 3 + 7 = 3 3 7 3 3 7 3 3 + 7 6 3 7 = 7 7 6 3 7 3 3 7 0 10 = = 10. To find: (-1)³ + (7)³ + (5)³ Since
More informationQUESTION 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 informationRMT 2013 Geometry Test Solutions February 2, = 51.
RMT 0 Geometry Test Solutions February, 0. Answer: 5 Solution: Let m A = x and m B = y. Note that we have two pairs of isosceles triangles, so m A = m ACD and m B = m BCD. Since m ACD + m BCD = m ACB,
More informationCBSE X Mathematics 2012 Solution (SET 1) Section D
Section D Q 9. A shopkeeper buys some books for Rs 80. If he had bought 4 more books for the same amount, each book would have cost Rs 1 less. Find the number of books he bought. Let the number of books
More informationLLT Education Services
Pract Quet 1. Prove th Equal chord of a circle ubted equal agle the cetre.. Prove th Chord of a circle which ubted equal agle the cetre are equal. 3. Prove th he perpedicular from the cetre of a circle
More informationTopic 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 informationMathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes
Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes Quiz #1. Wednesday, 13 September. [10 minutes] 1. Suppose you are given a line (segment) AB. Using
More informationEuclidian Geometry Grade 10 to 12 (CAPS)
Euclidian Geometry Grade 10 to 12 (CAPS) Compiled by Marlene Malan marlene.mcubed@gmail.com Prepared by Marlene Malan CAPS DOCUMENT (Paper 2) Grade 10 Grade 11 Grade 12 (a) Revise basic results established
More informationSample Question Paper Mathematics First Term (SA - I) Class IX. Time: 3 to 3 ½ hours
Sample Question Paper Mathematics First Term (SA - I) Class IX Time: 3 to 3 ½ hours M.M.:90 General Instructions (i) All questions are compulsory. (ii) The question paper consists of 34 questions divided
More informationCircle 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 informationSimilarity of Triangle
Similarity of Triangle 95 17 Similarity of Triangle 17.1 INTRODUCTION Looking around you will see many objects which are of the same shape but of same or different sizes. For examples, leaves of a tree
More informationTHEOREMS WE KNOW PROJECT
1 This is a list of all of the theorems that you know and that will be helpful when working on proofs for the rest of the unit. In the Notes section I would like you to write anything that will help you
More informationUnderstand and Apply Theorems about Circles
UNIT 4: CIRCLES AND VOLUME This unit investigates the properties of circles and addresses finding the volume of solids. Properties of circles are used to solve problems involving arcs, angles, sectors,
More informationPlane 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 informationTOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X
TOPPER SAMPLE PAPER 3 Summative Assessment-II MATHEMATICS CLASS X M.M: 80 TIME : 3-3 2 Hrs. GENERAL INSTRUCTIONS :. All questions are compulsory. 2. The question paper consists of 34 questions divided
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More informationGrade 5 Geometry. Answer the questions. Choose correct answer(s) from the given choices. Fill in the blanks
ID : cn-5-geometry [1] Grade 5 Geometry For more such worksheets visit www.edugain.com Answer the questions (1) What is the common term for the perimeter of a circle? (2) What is the perimeter of an isosceles
More information