Geometry Stumper

[Albert Chan]

I got the interesting problem from book Return of the Straight Dope

Solution is on the web (link below), but try not to peek.

Can Cecil solve this geometry stumper ?

Quote:Dear Cecil:

The following geometry problem has haunted me for 30 years. Every math teacher,
Ph.D., engineer, etc., I've shown it to was stumped. Now it's your turn.

Given any triangle ABC, extend the baseline and bisect the interior and exterior angles at A and B.
Extend these four new lines until they intersect at D and E. Prove DCE is a straight line.
(It looks straight, but no one can prove it.) How about it?

— John Ricketts, Madison, Wisconsin

Code:

 D
                 C
                                   E
             
            
         
 F       A ------------------ B    Z
             Triangle base

Point D:
Angle(FAC) = 2 * Angle(FAD)
Angle(ABC) = 2 * Angle(ABD)

Point E:
Angle(ZBC) = 2 * Angle(ZBE)
Angle(BAC) = 2 * Angle(BAE)

Prove: DCE is a straight line