MathDB
collinear wanted, altitudes, <QFD = < EPC, OH _|_ AQ

Source: 2020 Korea Junior Math Olympiad p4 KJMO

November 24, 2021
collineargeometry

Problem Statement

In an acute triangle ABCABC with AB‾>AC‾\overline{AB} > \overline{AC}, let D,E,FD, E, F be the feet of the altitudes from A,B,CA, B, C, respectively. Let PP be an intersection of lines EFEF and BCBC, and let QQ be a point on the segment BDBD such that ∠QFD=∠EPC\angle QFD = \angle EPC. Let O,HO, H denote the circumcenter and the orthocenter of triangle ABCABC, respectively. Suppose that OHOH is perpendicular to AQAQ. Prove that P,O,HP, O, H are collinear.
Back to ProblemsView on AoPS