# NCERT – CLASS 10 – CIRCLES – EXERCISE 10.2

EXERCISE QUESTIONS FROM NCERT TEXTBOOK

In Q.1 to 3, choose the correct option and give justification.

1. From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from

the centre is 25 cm. The radius of the circle is

(A) 7 cm (B) 12 cm

(C) 15 cm (D) 24.5 cm

In Fig. 10.11, if TP and TQ are the two tangents

to a circle with centre O so that ∠ POQ = 110°,

then ∠ PTQ is equal to

(A) 60° (B) 70°

(C) 80° (D) 90°

If tangents PA and PB from a point P to a circle with centre O are inclined to each other

at angle of 80°, then ∠ POA is equal to

(A) 50° (B) 60°

(C) 70° (D) 80°

1. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
1. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
1. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
1. Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
1. A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC
2. In Fig. 10.13, XY and X’Y’ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X’Y’ at B. Prove that ∠AOB = 90°.
1. Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
1. Prove that the parallelogram circumscribing a circle is a rhombus.
1. A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.
1. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.