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