Geometry Problem 1407: Right Triangle, Incircle, Excircle, Collinear
Tangency Points, Collinearity
The figure below shows a right triangle ABC (angle B = 90 degree). The
incircle I is tangent to AB at D. The excircle E corresponding to BC is
tangent to BC and AC extended at F and G, respectively. Prove that D, F,
and G are collinear.