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 PT is a tangent at T to a circle whose centre is O and OP = 17 cm, OT = 8 cm, find the length of the tangent segment PT.

Find the length of a tangent drawn to a circle with radius 5 cm, from a point 13 cm from the centre 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 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.