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$aPA^2+bPB^2+cPC^2$ is constant for P on incircle.

Source: ILL 1979-43

June 2, 2011
geometry proposedgeometry

Problem Statement

Let a,b,ca, b, c denote the lengths of the sides BC,CA,ABBC,CA,AB, respectively, of a triangle ABCABC. If PP is any point on the circumference of the circle inscribed in the triangle, show that aPA2+bPB2+cPC2aPA^2+bPB^2+cPC^2 is constant.
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