# CBSE 10 Mathematics Circles Practice Paper

1. The lengths of tangents drawn from an external point to a circle are equal.

2. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

3. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.

4. 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.

5. 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.

6. In Fig - 1, 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°.

7. 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.