Problem

Source: 2020 Korea Junior Math Olympiad p4 KJMO

Tags: collinear, geometry



In an acute triangle ABC with ¯AB>¯AC, let D,E,F be the feet of the altitudes from A,B,C, respectively. Let P be an intersection of lines EF and BC, and let Q be a point on the segment BD such that QFD=EPC. Let O,H denote the circumcenter and the orthocenter of triangle ABC, respectively. Suppose that OH is perpendicular to AQ. Prove that P,O,H are collinear.