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APMO 2016: Great triangle

Source: APMO 2016, problem 1

May 16, 2016
geometrycircumcircleAPMOgeometry solvedfunctional equationright trianglereflection

Problem Statement

We say that a triangle ABCABC is great if the following holds: for any point DD on the side BCBC, if PP and QQ are the feet of the perpendiculars from DD to the lines ABAB and ACAC, respectively, then the reflection of DD in the line PQPQ lies on the circumcircle of the triangle ABCABC. Prove that triangle ABCABC is great if and only if ∠A=90∘\angle A = 90^{\circ} and AB=ACAB = AC.
Senior Problems Committee of the Australian Mathematical Olympiad Committee
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