# The centers of tw

Given, CD is parallel to PQ, Two Circles with centers P and Q intersect at point A and B.

To Prove: 2PQ = CD

Construction: PE and QE are the Perpendiculars on the Chord CD From centers P and Q respectively.

DE = EA

CF = AF

DE + EA + AF + FC = DC

2EA + 2AF = DC

2(EA + AF) = DC ……..(1)

PQ and CD are parallel lines and PE and QE are the perpendiculars.

So, AEP = 900,AFQ = 900,EPQ = 900,AFQ = 900

EPQF is a rectangle

So, EF = PQ ……… (2)

2(EA + AF) = DC

2EF = DC

2PQ = DC

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