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cyclic quadrilateral with orthocenter and circumcenter

Source: 2022 Centroamerican and Caribbean Mathematical Olympiad, P3

December 1, 2022
geometrycircumcircleorthocentercyclic quadrilateral

Problem Statement

Let ABCABC an acutangle triangle with orthocenter HH and circumcenter OO. Let DD the intersection of AOAO and BHBH. Let PP be the point on ABAB such that PH=PDPH=PD. Prove that the points B,D,OB, D, O and PP lie on a circle.
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