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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
Also,
In
AQM, using Pythagoras theorem
From 1 and 2, we get
Put,x=0 in equation 1