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Yet another circle!

Source: INMO 1999 Problem 4

October 7, 2005
trigonometrycomplex numbersgeometry solvedgeometry

Problem Statement

Let Γ\Gamma and Γ′\Gamma' be two concentric circles. Let ABCABC and A′B′C′A'B'C' be any two equilateral triangles inscribed in Γ\Gamma and Γ′\Gamma' respectively. If PP and P′P' are any two points on Γ\Gamma and Γ′\Gamma' respectively, show that P′A2+P′B2+P′C2=A′P2+B′P2+C′P2. P'A^2 + P'B^2 + P'C^2 = A'P^2 + B'P^2 + C'P^2.
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