Let ABC be a triangle. The incircle of ABC touches BC,AC,AB at D,E,F, respectively. Each pair of the incircles of triangles AEF,BDF,CED has two pair of common external tangents, one of them being one of the sides of ABC. Show that the other three tangents divide triangle DEF into three triangles and three parallelograms. geometrygeometric transformationreflectionincenterparallelogramgeometry proposed