IMO 1979 LL ISR43

Let a, b, c denote the lengths of the sides BC, CA, AB, respec-

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IMO 1979 LL ISR43

Origin: ISR

Problem

Let a, b, c denote the lengths of the sides BC, CA, AB, respec- tively, of a triangle ABC. If P is any point on the circumference of the circle inscribed in the triangle, show that aPA2+bPB2+cPC2 is constant.