Let ABC be an acute scalene triangle. Incircle of ABC touches BC,CA,AB at D,E,F respectively. Let X,Y,Z be feet the altitudes of from A,B,C to the sides BC,CA,AB respectively. Let A′,B′,C′ be the reflections of X,Y,Z in EF,FD,DE respectively. Prove that triangles ABC and A′B′C′ are similar. geometrysimilar triangles