Let ABC be a right-angled triangle in A such that AB<AC. Let M be the midpoint of BC and let D be the intersection of AC with the perpendicular line to BC which passes through M. Let E be the intersection point of the parallel line to AC which passes through M with the perpendicular line to BD which passes through B. Prove that triangles AEM and MCA are similar if and only if ∠ABC=60∘. geometrygeometry proposed