University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2021
Views:

400

Pages:

3
Author:

Nesbyenvkk

EXERCISE # 1 Q.1 Q.7 If a diameter of a circle bisects each of the two chords of a circle, prove that the chords are parallel. Q.8 In figure, if The radius of a circle is 13 cm and the length of one of its chords is 10 cm. Find the distance of  , prove that A = B. the chord from the centre. Q.2 Find the length of a chord which is at a distance O of 5 cm from the centre of a circle of radius 13 A cm. Q.3 B In figure two equal chords AB and CD of a circle with centre O, intersect each other at E. Q.9 Prove that AD = CB. A In figure O is the centre of a circle and PO O P B A, B, C, D are four consecutive points on a circle such that AB = CD. Prove that AC = BD. Two equal circles intersect in P and Q. A straight line through P meets the circles in A and B. Prove that QA = QB. Q.11 Bisector AD of BAC of ABC passes through the centre O of the circumcircle of 5 cm. OP AB, OQ  CD, AB || CD, ABC as shown in figure. Prove that AB = AC. A AB = 6 cm and CD = 8 cm. Determine PQ. P Q C Q.10 In Figure O is the centre of the circle of radius A E F B C C A D D E Q.5 C bisects APD. Prove that AB = CD O Q.4 D B D O O B Q. 6 In Figure O is the centre of the circle of radius 5 cm. OP  AB, OQ  CD, AB || CD, AB = 6 Q.12 C D In figure calculate the measure of AOC. B cm and CD = 8 cm. Determine PQ. A P B 30º A O C Q D O 40º C Q.13 In figure A, B, and C are three points on a sides AB and AC at D and E respectively. circle such that the angles subtended by the Prove that DE || BC. chords AB and AC at the centre O are 90º and 110º, respectively. Determine BAC. Q.20 A In fig. A = 60º and ABC = 80º, find DPC and BQC. P 90º B 110º O D C C Q.14 A Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter B Q bisects the base. Q.15 In figure A, B, C are three points on a circle Q.21 such that the angles subtended by the chord AB In fig. A, B, C and D, E, F are two sets of collinear points, Prove that AD || CF. and AC at the centre O are 80º and 120º respectively. Determine BAC. A A 80º B 3 1 D 2 120º O C B E C F Q.22 In fig. ABCD is a cyclic quadrilateral. A circle passing through A and B meets AD and BC in Q.16 In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6 cm. Find the the points E and F respectively. Prove that EF || DC. length of the chord BC. A Q.17 E Prove that the line joining the mid-points of 2 two parallel chords of a circle passes through 3 D the centre. C Q.18 In Figure  circle. Prove that OA is the perpendicular bisector of BC. Q.19 1 and O is the centre of the In an isosceles triangle ABC with AB = AC, a circle passing through B and C intersects the B F ANSWER KRY A. VERY SHORT ANSWER TYPE QUESTIONS : 1. 12 cm 2. 24cm B. SHORT ANSWER TYPE QUESTIONS : 5. 1 cm 6. 7 cm C. LONG ANSWER TYPE QUESTIONS : 16. 9.6 cm 20. 40º, 20º 12. 70º 13. 80º 15. 80º