Let C be a circle in plane. Let C1 and C2 be nonintersecting circles touching C internally at points A and B respectively. Let t be a common tangent of C1 and C2 touching them at points D and E respectively, such that both C1 and C2 are on the same side of t. Let F be the point of intersection of AD and BE. Show that F lies on C. geometryangle bisectorgeometry proposed