Geometry Problem 1409: Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity

Proposition

The figure below shows a right triangle ABC (angle B = 90 degree) with the incircle I tangent to AC and BC at D and F, respectively. The excircle E corresponding to BC is tangent to AB extended at G. Prove that D, F, and G are collinear points.
 
 

Geometry Problem 1409: Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity, Tutor

 

See also: Typography and poster of problem 1408.