In the following figure, AD is a straight line. OP ⊥ AD and O is the centre of both the circles. If OA = 34 cm, OB = 20 cm and OP = 16 cm; find the length of AB.

In a circle of radius 17 cm, two parallel chords of lengths 30 cm and 16 cm are drawn. Find the distance between the chords, if both the chords are :

(i) on the opposite sides of the center,

(ii) on the same side of the center.

A chord CD of a circle, whose center is O, is bisected at P by a diameter AB.

Given OA = OB = 15 cm and OP = 9 cm. Calculate the lengths of :

(i) CD

(ii) AD

(iii) CB.

A straight line is drawn cutting two equal circles and passing through the mid-point M of the line joining their centers O and O'.

Prove that the chords AB and CD, which are intercepted by the two circles, are equal.