Circles and the Euler line
Source: 2020 Iberoamerican #6
November 17, 2020
geometry
Problem Statement
Let be an acute, scalene triangle. Let be the orthocenter and be the circumcenter of triangle , and let be a point interior to the segment The circle with center and radius intersects the lines and again at and , respectively. Denote by the symmetric point of with respect to the perpendicular bisector of . Prove that points , , and lie on the same circle.