Important questions of Maths class 10 chapter 10 |Extra questions of Maths class 10 chapter 10 Circles

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

Important questions of Maths class 10 chapter 10

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.