There are two circles: $C1$ and $C2$. They touch internally at point B (note that C1 is inside of C2). C1 has a chord BC, which is produced to meet C2 at D. The tangent from C meets the common tangent from B at point E. There's a point F, which is where C2 and line CE intersect each other in a manner that causes E and F to be on opposite sides of BC. The line BF meets C1 at G, and CG meets the tangent from D at H. From this information, I need to show that CFDH is a parallelogram.
This is what I've done so far:
I know I still need to prove that CH and DF are also parallel to prove that CFDH is a parallelogram, but I'm a little stuck on how to do this. Also, I don't know if my diagram correctly represents the given information... Some help would really be appreciated.