Typography of Geometry Problem 1374: Isosceles Triangle, Exterior Cevian, Incircle, Excircle, Tangency Points, Parallel Lines, iPad Apps

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 solution below

See also:
Original problem 1374.

Geometric Art using iPad or Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.