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Reflection of D moves on a line

Source: KöMaL A. 705

November 11, 2017
geometrygeometric transformationreflection

Problem Statement

Triangle ABCABC has orthocenter HH. Let DD be a point distinct from the vertices on the circumcircle of ABCABC. Suppose that circle BHDBHD meets ABAB at P≠BP\ne B, and circle CHDCHD meets ACAC at Q≠CQ\ne C. Prove that as DD moves on the circumcircle, the reflection of DD across line PQPQ also moves on a fixed circle.
Michael Ren
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