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Prove that the Euler line HU bisects the angle BHD

Source: Austrian Mathematical Olympiad 2000, Part 2, D2, P1

June 28, 2011
Eulergeometrycircumcircleangle bisectorgeometry proposed

Problem Statement

In a non-equilateral acute-angled triangle ABCABC with ∠C=60∘\angle C = 60^\circ, UU is the circumcenter, HH the orthocenter and DD the intersection of AHAH and BCBC. Prove that the Euler line HUHU bisects the angle BHDBHD.
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