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.

Two equal chords AB and CD of a circle with center O, intersect each other at point P inside the circle. Prove that :

(i) AP = CP

(ii) BP = DP

In the following figure, OABC is a square. A circle is drawn with O as center which meets OC at P and OA at Q. Prove that :

(i) △ OPA ≅ △ OQC

(ii) △ BPC ≅ △ BQA