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EXERCISE – 19

Q. 1. In the given figure, PQ is a diameter of the circle whose centre is O. Given Calculate

Q. 2. In the given diagram a chord ED is parallel to the diameter AC of the circle ABCDE. If Calculate .

Q. 3. In the given figure, Calculate

Q. 4. In the above figure, O is the centre of the circle. calculate the value of

Q. 5. In the given figure, A, B, C, D lie on a circle with centre O. Arc AB = 2 Arc BC. Calculate

Q. 6. In the given figure; AC is the diameter of the circle with centre O. CD and BE are parallel, Calculate

Q. 7. In the adjoining figure, AD is diameter of the circle with centre O. OB is parallel to DC and . Calculate the numerical value of

1. 
2. and
3. 

Q. 8. C is point on the minor arc AB of the circle with centre O. express q in terms of p. Calculate p if ACBO is a parallelogram.

Q. 9. In the given diagram, Calculate

Q. 10. In the given diagram AD is a diameter of the circle ABD. Chords AB and CD meet at P, Find the angle

Q. 11. In the figure given, ABCD is a cyclic quadrilateral in which Calculate

Q. 12. In the adjoining diagram, AB is a diameter of the circle whose centre is O. Given that calculate

Q. 13. In the adjoining diagram, O is the centre of the circle. If , find the value of p, q and r.

Q. 14. ABCD is a cyclic quadrilateral in which Find

Q. 15. In this figure, AD is the diameter of the circle. If , calculate

Q. 16. In the figure, O is the centre of the circle. and XY is parallel to TZ. Find giving reason

Q. 17. ABCD is a cyclic quadrilateral; AD = DC. Calculate

Q. 18. O is the centre of the circle; A, B and C are points on the circumference.

1. If x = 60⁰, calculate y
2. State the general equation relating x and y.

Q. 19. O is the centre of the circle and BOC is a diameter. Write down the value of the angle AOC.

Q. 20. In the figure, O is the centre of the circle. Calculate the angles

1. DOE
2. DBE
3. ABD.

Q. 21. In the given circle with diameter AB, find the value of x.

Q. 22. In the given figure, AB is a diameter of the circle. Find Given reasons for your answer.

Q. 23. In the adjoining figure, AC is the diameter of a circle with centre O. Chord BD is perpendicular to AC. Write down the angles p, q, r in terms of x.

Q. 24. In the given figure, O is the centre of the circle. If

Q. 25. In the given figure, O is the centre of the circle. If

Q. 26. In the given figure, O is the centre of the circle, AOB is a diameter. If

Q. 27. In the given figure, O is the centre of a circle and ABE is a straight line. If , Find:

1. 
2. 
3. The value of x.

Q. 28. In the given figure, AB and CD are two parallel chords of a circle. If BDE and ACE are straight lines, intersecting at E, prove that isosceles.

Q. 29. In the given figure, the two circles intersect at P and Q. If

calculate

Q. 30. In the adjoining figure, AB = AC = CD, , calculate

Answers
1. 690	2. 270
3. (i) 760 (ii) 280	4. 480
5. (i) 540 (ii) 270 (iii) 1260	6. (i) 500 (ii) 1000 (iii) 300
7. (i)900 (ii) 300 (iii) 600	8. (i) q0 = 3600 – 2p0, p = 1200
9. (i) 500 (ii) 900 (iii) 400	10. 300
11. (i) 270 (ii) 830 (iii) 700	12. (i) 640 (ii) 640
13. p = 1500, q = 600, r = 300	14. (i) 300 (ii) 1050 (iii) 470
15. (i) 500 (ii) 400	16. (i) 250 (ii) 250 (iii) 500
17. (i) 500 (ii) 1300 (iii)250	18. (i) 2400 (ii) y = 3600 – 2x
19. 1140	20. (i) 1100 (ii) 250 (iii) 350
21. 600	22. 2700
23.	24. 500
25. 950	26. 400
27. (i) 550 (ii) 1250 (iii) 2500	29. (i) 1000 (ii) 960
30. (i) 700 (ii) 400

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