Geometry Problem 1374: Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines.

Proposition

In the figure below, ABC is an isosceles triangle (AB = BC) and D is a point on CA extended, The Incircle E of the triangle DAB is tangent to BD at F. The excircle G of the triangle DBC is tangent to AC extended at H. Prove that BG and FH are parallel.

BD is called an exterior cevian of triangle ABC.
 

Geometry Problem 1374: Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines
See also:
Typography of problem 1374