Two circles whose centres are O and O' intersect at P. Through P, line "l" parallel to OO' intersecting the circles at C and D is drawn. Prove that CD=2OO'.
To Prove : CD = 2OO'
1. Draw perpendicular PG from point P on OO'
2. Draw perpendiculars OE and O'F from O and O' on CD.
CE=EP ( perpendicular from the centre of a circle to a chord bisects the chord)
OO' || CD ( given )
and OE || GP || O'F ( all are perpendiculars on the line CD )
EP = OG and PF = GO'