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PO = HQ wanted, <BAC = 60^o, circumcenter, orthocenter

Source: OIFMAT II 2012 day 1 p4 - Chilean Math Forum FMAT Olympiad https://artofproblemsolving.com/community/c2484778_oifmat

September 27, 2021
geometryCircumcenterorthocenterequal segments

Problem Statement

Given a △ABC \vartriangle ABC with AB>AC AB> AC and ∠BAC=60o \angle BAC = 60^o. Denote the circumcenter and orthocenter as O O and H H respectively. We also have that OH OH intersects AB AB in P P and AC AC in Q Q . Prove that PO=HQ PO = HQ .
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