Challenge 378: Triple Triangle Teaser
Can you prove this geometrical result for a particular trio of triangles?
Triangle ABC is isosceles with angle BAC = 20o and AB = AC.
Point D, which is closer to C than B, is positioned so that triangle ADC is also isosceles, with DA = DC.
Points B, C and F lie on the same straight line, with C in between B and F, and triangle CDF is equilateral.
Prove that AB = BC + DC.
Justify each step in your solution clearly!