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HMMT Team 2019/6: A real geometry problem

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February 17, 2019
HMMTgeometry

Problem Statement

Scalene triangle ABCABC satisfies ∠A=60∘\angle A = 60^{\circ}. Let the circumcenter of ABCABC be OO, the orthocenter be HH, and the incenter be II. Let DD, TT be the points where line BCBC intersects the internal and external angle bisectors of ∠A\angle A, respectively. Choose point XX on the circumcircle of △IHO\triangle IHO such that HX∥AIHX \parallel AI. Prove that OD⊥TXOD \perp TX.
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