MathDB

6

Part of 2015 EGMO

Problems(1)

reflection with circumcentre EGMO P6

Source: EGMO 2015, Problem 6

4/17/2015
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'
geometrycircumcircleEGMOorthocenterCentroidanglesEGMO 2015