If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

A point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

If from any point on the common chord of two intersecting circles, tangents be drawn to the circles, prove that they are equal.

If AB, AC, PQ are tangents in Fig. 10.51 and AB = 5 cm, find the perimeter of .

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