Let ABC be an acute triangle and let A1,B1,C1 be the feet of its altitudes. The incircle of the triangle A1B1C1 touches its sides at the points A2,B2,C2. Prove that the Euler lines of triangles ABC and A2B2C2 coincide. Eulergeometryincenterprojective geometrygeometric transformationhomothetycircumcircle