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angle wanted, orthocenter, circumcenter, circle (H,HA)

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2018 Shortlist G1 day1

September 22, 2021
geometryCircumcenterorthocenterangles

Problem Statement

Let HH be the orthocenter and OO the circumcenter of the acute triangle △ABC\vartriangle ABC. The circle with center HH and radius HAHA intersects the lines ACAC and ABAB at points PP and QQ, respectively. Let point OO be the orthocenter of triangle △APQ\vartriangle APQ, determine the measure of ∠BAC\angle BAC.
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