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Prove that H, O and D are collinear

Source: Chinese TST, Test 3, Problem 1 2012

March 25, 2012
geometrycircumcircletrigonometryChina

Problem Statement

In an acute-angled ABCABC, ∠A>60∘\angle A>60^{\circ}, HH is its orthocenter. M,NM,N are two points on AB,ACAB,AC respectively, such that ∠HMB=∠HNC=60∘\angle HMB=\angle HNC=60^{\circ}. Let OO be the circumcenter of triangle HMNHMN. DD is a point on the same side with AA of BCBC such that △DBC\triangle DBC is an equilateral triangle. Prove that H,O,DH,O,D are collinear.
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