Let ABC be a triangle. P, Q and R are the points of contact of the incircle with sides AB, BC and CA, respectively. Let L, M and N be the feet of the altitudes of the triangle PQR from R, P and Q, respectively.
a) Show that the lines AN, BL and CM meet at a point.
b) Prove that this points belongs to the line joining the orthocenter and the circumcenter of triangle PQR.
Aarón Ramírez, El Salvador geometrycircumcircleincentergeometric transformationhomothetyEulergeometry proposed