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Yet another cyclic quadrilateral

Source: European Mathematical Cup 2012, Senior Division, Problem 2

July 27, 2013
geometrygeometric transformationreflectioncircumcirclegeometry proposed

Problem Statement

Let ABCABC be an acute triangle with orthocenter HH. Segments AHAH and CHCH intersect segments BCBC and ABAB in points A1A_1 and C1C_1 respectively. The segments BHBH and A1C1A_1C_1 meet at point DD. Let PP be the midpoint of the segment BHBH. Let D′D' be the reflection of the point DD in ACAC. Prove that quadrilateral APCD′APCD' is cyclic.
Proposed by Matko Ljulj.
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