MathDB
Shortlist 2017/G3

Source: Shortlist 2017, Moldova TST 2018

July 10, 2018
geometryIMO ShortlistAngle Chasingprojective geometrysimilar trianglesISL 2017G3

Problem Statement

Let OO be the circumcenter of an acute triangle ABCABC. Line OAOA intersects the altitudes of ABCABC through BB and CC at PP and QQ, respectively. The altitudes meet at HH. Prove that the circumcenter of triangle PQHPQH lies on a median of triangle ABCABC.
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