AFA_1C is cyclic iff BF bisects CG, orthocenter, parallelogram related
Source: 2013 Croatia MO p3
August 5, 2020
geometryparallelogrambisectscyclic quadrilateralConcyclicbisects segment
Problem Statement
Given a pointed triangle with orthocenter . Let be the point such that the quadrilateral is parallelogram. Let be the perpendicular to the direction through the midpoint of the side . Denote the intersection of the lines and with , and the midpoint of the length with . The point where the parallel to the line through point intersects denote by . Prove that the quadrilateral is cyclic if and only if the lines passes through the midpoint of the length .