Geometry Stumper

[Albert Chan]

PHP Code:

c = {1, Tan[t2/2]}; 
e = {1 - Tan[t2/2] Tan[t3/2], Tan[t2/2] + Tan[t3/2]}; (* excircle center *) 


This prove is even shorter !

Dot[c, e-c] = 1 * -tan(t2/2) tan(t3/2) + tan(t2/2) * tan(t3/2) = 0

-> OCE is right triangle -> by symmetry, OCD also right triangle -> CDE is straight line