Problem

Source: RomNO 2019, grade ix, p.1

Tags: Pure geometry, vectorial geometry, geometry, perpendicular bisector



Let be a point $ P $ in the interior of a triangle $ ABC $ such that $ BP=AC, M $ be the middlepoint of the segment $ AP, R $ be the middlepoint of $ BC $ and $ E $ be the intersection of $ BP $ with $ AC. $ Prove that the bisector of $ \angle BEA $ is perpendicular on $ MR $