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reflection with circumcentre EGMO P6

Source: EGMO 2015, Problem 6

April 17, 2015
geometrycircumcircleEGMOorthocenterCentroidanglesEGMO 2015

Problem Statement

Let HH be the orthocentre and GG be the centroid of acute-angled triangle ABCABC with AB≠ACAB\ne AC. The line AGAG intersects the circumcircle of ABCABC at AA and PP. Let P′P' be the reflection of PP in the line BCBC. Prove that ∠CAB=60\angle CAB = 60 if and only if HG=GP′HG = GP'
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