EXERCISE
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 4 cm and the distance of Q from the centre is 5 cm. The radius of the circle is (A) 7cm (B) 3cm (C) 5cm (D) 4.5cm 2. In fig, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 90°, then ∠PTQ is equal to (A) 60° (B) 70° (C) 80° (D) 90° 3. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 60°, then ∠POA is equal to (A) 50° (B) 60° (C) 70° (D) 80° 4. Prove that the tangents drawn at the ends of a diameter of a circle are parallel. 5. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre. 6. The length of a tangent from a point A at distance 15 cm from the centre of the circle is 12 cm. Find the radius of the circle. 7. 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. 8. Aquadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD =AD + BC 9. 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°. 10. 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. 11. Prove that the parallelogram circumscribing a circle is a rhombus. 12. Atriangle 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 sidesAB and AC. 13. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.Solution