Problem

Source: Centroamerican 2012, Problem 2

Tags: geometry, circumcircle, trapezoid, perpendicular bisector, geometry unsolved



Let γ be the circumcircle of the acute triangle ABC. Let P be the midpoint of the minor arc BC. The parallel to AB through P cuts BC,AC and γ at points R,S and T, respectively. Let KAPBT and LBSAR. Show that KL passes through the midpoint of AB if and only if CS=PR.