MathDB

G2

Part of 2019 Costa Rica - Final Round

Problems(1)

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

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

9/22/2021
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.
geometryCircumcenterorthocenterangles