## CBSE Class 10 Maths Chapter-10 Circles – Free PDF Download

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

**CBSE Class 10 Maths Important Questions Chapter 10 – Circles**

**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