## Important questions of Maths class 10 chapter 10

CLASS – X

CHAPTER – 10 CIRCLES

SESSION: 2022-23

MULTIPLE CHOICE QUESTIONS

1. The length of the tangent drawn from a point 8 cm away from the centre of circle of radius 6 cm is _____

a) √7 cm b) 2√7 cm c) 10 cm d) 5cm

2. AOB is a diameter of a circle with centre O and AC is a tangent to the circle at A. If BOC =

130°, then find ACO

a) 400 b) 600 c) 900 d) 800

3. If the angle between two radii of a circle is 1300, then the angle between the tangents at the end is _____

a) 500 b) 600 c) 700 d) 800

4. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is

a) 3 cm b) 6 cm c) 9 cm d) 1 cm

5. If angle between two tangents drawn from a point P to a circle of radius a and centre O is 600, then OP = ___

a) 2a b) a√3 c) a√2 d) 3a

6. A quadrilateral ABCD is drawn to circumscribe a circle. If AB = 12cm, BC = 15 cm and CD = 14 cm, then AD = ____

a) 11 cm b) 12 cm c) 13 cm d) 14 cm

SUBJECTIVE QUESTIONS

7. Prove that the lengths of tangents drawn from an external point to a circle are equal

8. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle.

9. If the angle between two tangents drawn from an external point P to circle of radius ‘a’ and centre ‘O’ is 600, then find the length OP.

10. If an isosceles triangle ABC, in which AB =AC = 6 cm, is inscribed in a circle of radius 9 cm. Find the area of triangle.

11.In given figure, a circle is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF

12. The incircle of ABC touches the sides BC, CA and AB at D, E and F respectively. Show that

AF + BD + CE = AE + BF + CD = (Perimeter of ∆𝐴𝐵𝐶)

13. In figure, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

14.In figure, CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R. If CP = 11 cm and BR = 4 cm, find the length of BC.

15. In the given figure, two tangents PA and PB are drawn to a circle with centre O from an external point P. Prove that APB = 2 OAB

16. Two tangents RQ and RP are drawn from an external point R to a circle with centre O. If ∠PRQ = 120⁰, then prove that OR = PR + RQ.

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