KöMaL 2006 K83

Consider a convex hexagon in the plane with four distinct points given in its interior, such that no three points out of the vertices of the hexagon and the four given points lare collinear. The hexagon is dissected into triangles, such that the vertices are those of the hexagon and the given points. (All the 10 points must be used.) Show that the number of triangles obtained is always 12.