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)
Similarly, PF=FD  
OO' || CD  ( given )
and OE || GP || O'F  ( all are perpendiculars on the line CD ) 
EP = OG and PF = GO' 

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