Problem

Source: Slovenia IMO TST 2018, Day 1, Problem 4

Tags: geometry, circumcircle



Let K be a circle centered in A. Let p be a line tangent to K in B and let a line parallel to p intersect K in C and D. Let the line AD intersect p in E and let F be the intersection of the lines CE and AB. Prove that the line through D, parallel to the tangent through A to the circumcircle of AFD intersects the line CF on K.