  # Important Questions for CBSE Class 10 Maths Chapter 10 - Circles 1 Mark Question

Free PDF download of Important Questions with Answers for CBSE Class 10 Maths Chapter 10 – Circles prepared by expert Maths teachers from latest edition of CBSE(NCERT) books only by CoolGyan to score more marks in CBSE board examination.

CBSE Class 10 Maths Chapter-10 Circles Important Questions

## 1 Mark Questions

1. How many tangents can a circle have?
Ans. A circle can have infinitely many tangents since there are infinitely many points on the circumference of the circle and at each point of it, it has a unique tangent.

2. The perimeter of a sector of a circle of radius 8 cm is 25m, what is area of sector?
(a) (b) (c) (d) none of these
Ans. (a) 3. In figure given below PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PA = 10cm and DQ = 2cm. What is length of PC?
(a) 8 cm
(b) 7 cm
(c) 4 cm
(d) none of these Ans. (a) 8 cm

4. Tangent of circle intersect the circle
(a) Only one point
(b) Two points
(c) Three points
(d) None of these
Ans. (a) Only one point

5. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25cm. The radius of the circle is
(a) 7 cm
(b) 12 cm
(c) 15 cm
(d) 24.5 cm
Ans. (a) 7 cm

6. How many tangents can a circle have?
(a) 1
(b) 2
(c) 0
(d) infinite
Ans. d) infinite

7. If PA and PB are tangents from a point P lying outside the circle such that PA = 10 cm and . Find length of chord AB.
(a) 10 cm
(b) 20 cm
(c) 30 cm
(d) 40 cm
Ans. (a) 10cm

8. A tangent PQ at a point P to a circle of radius 5 cm meets a line through the centre O at a point Q, so that OQ = 13cm, then length of PQ is
(a) 11 cm
(b) 12 cm
(c) 10 cm
(d) None of these
Ans. (b) 12 cm

9. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of , then is equal to
(a) 50 (b) 60 (c) 70 (d) 80 Ans. (a) 50 10. How many tangents can a circle have?
(a) 1
(b) 2
(c) 0
(d) infinite
Ans. (d) infinite

11. If PA and PB are tangents from a point P lying outside the circle such that PA = 10 cm and . Find length of chord AB.
(a) 10 cm
(b) 20 cm
(c) 30 cm
(d) 40 cm
Ans. (a) 10 cm

12. A tangent PQ at a point P to a circle of radius 5 cm meets a line through the centre O at a point Q, so that OQ = 13cm, then length of PQ is
(a) 11 cm
(b) 12 cm
(c) 10 cm
(d) None of these
Ans. (b) 12 cm

13. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of , then is equal to
(a) 50 (b) 60 (c) 70 (d) 80 Ans. (a) 50 14. The length of tangent drawn to a circle with radius 3 cm from a point 5 cm from the centre of the circle is
(a) 6 cm
(b) 8 cm
(c) 4 cm
(d) 7 cm
Ans. (c) 4 cm

15. A circle touches all the four sides of a quadrilateral ABCD whose sides AB = 6 cm, BC = 7 cm, CD = 4 cm,then AD = ____
(a) 2 cm
(b) 3 cm
(c) 5 cm
(d) 6 cm
Ans. (b) 3 cm

16. If a point lies on a circle, then what will be the number of tangents drawn from that point to the circle?
(a) 1
(b) 2
(c) 3
(d) infinite
Ans. (a) 1

17. A quadrilateral ABCD is drawn to circumscribe a circle IF AB = 4 cm, CD = 7 cm, BC = 3 cm, then length of AD is
(a) 7 cm
(b) 2 cm
(c) 8 cm
(d) none of these
Ans. (c) 8 cm

18. A tangent PQ at point P of a circle of radius 12 cm meets a line through the centre O to a point Q so that OQ = 20 cm, thenlength of PQ is
(a) 14 cm
(b) 15 cm
(c) 16 cm
(d) 10 cm
Ans. (d) 10 cm

19. A line intersecting a circle in two points is called
(a) tangent
(b) secant
(c) diameter
(d) none of these
Ans. (b) secant

20. The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. What will be the radius of circle?
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) none of these
Ans. (c) 3 cm

21. In the figure given below, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 12 cm and CQ = 3 cm, what is the length of PC?
(a) 9 cm
(b) 10 cm
(c) 1 cm
(d) 13 cm Ans. (a)
9 cm

22. The tangent of a circle makes angle with radius at point of contact
(a) 60 (b) 30 (c) 90 (d) none of these
Ans. (c) 90 23. If tangent PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 80 , then what is the value of (a) 30 (b) 50 (c) 70 (d) 90  Ans. (b)
50 