2021 EGMO P3: E, F, N, M lie on a circle
Source: 2021 EGMO P3
April 13, 2021
EGMO 2021geometryTriangleEGMO
Problem Statement
Let be a triangle with an obtuse angle at . Let and be the intersections of the external bisector of angle with the altitudes of through and respectively. Let and be the points on the segments and respectively such that and . Prove that the points lie on a circle.