Problem

Source: Mathematics Regional Olympiad of Mexico West 2021 P5

Tags: perpendicular, geometry



Let ABC be a triangle such that AC is its shortest side. A point P is inside it and satisfies that BP=AC. Let R be the midpoint of BC and let M be the midpoint of AP. Let E be the intersection of BP and AC. Prove that the bisector of angle BEA is perpendicular to segment MR.