MathDB
Many 60 degrees

Source: 2019 Brazil Ibero TST P1

June 14, 2023
geometryorthocentercircumcircleEquilateral Trianglecollinear

Problem Statement

Let ABCABC be an acute triangle, with ∠A>60∘\angle A > 60^\circ, and let HH be it's orthocenter. Let MM and NN be points on ABAB and ACAC, respectively, such that ∠HMB=∠HNC=60∘\angle HMB = \angle HNC = 60^\circ. Also, let OO be the circuncenter of HMNHMN and DD be a point on the semiplane determined by BCBC that contains AA in such a way that DBCDBC is equilateral. Prove that HH, OO and DD are collinear.
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