### Proposition

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

*BD is called an interior
cevian of triangle ABC.*