# Q : 1    Two circles of radii and intersect at two points and the distance between their  centres is . Find the length of the common chord.

Given: Two circles of radii and intersect at two points and the distance between their centres is .

To find the length of the common chord.

Construction: Join OP and draw

Proof: AB is a chord of circle C(P,3)  and PM is the bisector of chord AB.

Let, PM = x , so QM=4-x

In APM, using Pythagoras theorem

...........................1

Also,

In AQM, using Pythagoras theorem

...........................2

From 1 and 2, we get

Put,x=0 in equation 1

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