Problem

Source: V.A. Yasinsky Geometry Olympiad 2023 VIII p1 , Ukraine

Tags: geometry



Let O be the circumcenter of triangle ABC and the line AO intersects segment BC at point T . Assume that lines m and passing through point T are perpendicular to AB and AC respectively. If E is the point of intersection of m and OB and F is the point of intersection of and OC, prove that BE=CF. (Oleksii Karliuchenko)