Let ABC be a triangle and A′,B′,C′ the points in which its incircle touches the sides BC,CA,AB, respectively. We denote by I the incenter and by P its projection onto AA′. Let M be the midpoint of the line segment [A′B′] and N be the intersection point of the lines MP and AC. Prove that A′Nis parallel to B′C′ geometryincenterincircleparallel