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A^2 + b^2 + c^2 is a perfect square

Source: BWM 2004, 1st round, problem 2

September 2, 2004
geometry

Problem Statement

Consider a triangle whose sidelengths aa, bb, cc are integers, and which has the property that one of its altitudes equals the sum of the two others. Then, prove that a2+b2+c2a^2+b^2+c^2 is a perfect square.
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