MathDB
Another cyclic quad

Source: KoMaL A. 729

October 11, 2018
geometry

Problem Statement

In a cyclic quadrilateral ABCDABCD, the diagonals meet at point EE, the midpoint of side ABAB is FF, and the feet of perpendiculars from EE to the lines DA,ABDA,AB and BCBC are P,QP,Q and RR, respectively. Prove that the points P,Q,RP,Q,R and FF are concyclic.