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Mathematical Reflections

Source: 2019 Taiwan TST Round 1

March 31, 2020
geometry proposedgeometry

Problem Statement

Given a triangle △ABC \triangle ABC . Denote its incenter and orthocenter by I,H I, H , respectively. If there is a point K K with AH+AK=BH+BK=CH+CK AH+AK = BH+BK = CH+CK Show that H,I,K H, I, K are collinear.
Proposed by Evan Chen
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