### 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.*

See also:

Typography of problem 1374.