In the given figure, O is the center of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the :

(i) the radius of the circle

(ii) length of chord CD.

AB and CD are two equal chords of a circle with center O which intersect each other at right angle at point P. If OM ⊥ AB and ON ⊥ CD; show that OMPN is a square.

Prove that equal chords of congruent circles subtend equal angles at their centers.

Draw two circles of different radii. How many points these circles can have in common? What is the maximum number of common points ?