Question -28

Geometry Level 3

A rectangular hyperbola whose center is C C , is cut by any circle of radius r r in four points P , Q , R , S P,Q,R,S . then find the value of ( C P ) 2 + ( C Q ) 2 + ( C R ) 2 + ( C S ) 2 (CP)^2+(CQ)^2+(CR)^2+(CS)^2

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r 2 r^2 3 r 2 3 r^2 4 r 2 4 r^2 2 r 2 2 r^2

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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1 solution

Kislay Raj
Mar 3, 2015

Take the centre of the circle to be C C (For simplicity). Then distance from C C (which is now the centre of the circle) to the point of intersections P , Q , R P,Q,R and S S will be equal to the radius r r of the circle.

Then ( C P ) 2 + ( C Q ) 2 + ( C R ) 2 + ( C S ) 2 = 4 r 2 (CP)^2 + (CQ)^2 + (CR)^2 + (CS)^2 = 4r^2

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