Let ABC be a triangle, and let D, E, F be the points of contact of its incircle ω with its sides BC, CA, AB, respectively. Let K be the point of intersection of the line AD with the incircle ω different from D, and let M be the point of intersection of the line EF with the line perpendicular to AD passing through K. Prove that AM is parallel to BC. geometryreflectionincentercircumcircleradical axis