In the given figure two circles whose centres O and O’ intersect at P. Through P, a line parallel to OO’ intersecting the circles at C and D is drawn as shown. Prove that CD = 200’.

Given Given circles having centres O and O’ intersect at P.

Also CD ||OO’.

To prove CD = 2OO’

Construction Draw OA and O’B perpendicular to CD from O and O’, respectively.

Proof OA⊥CD

∴OA bisects the chord.

Also, CP is perpendicular from the centre to the chord bisects the chord.