Problem

Source: 2019 Taiwan TST Round 1

Tags: geometry proposed, geometry



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