Geometry Problem 1407: Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity

Proposition

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.

 
 

Geometry Problem 1407: Right Triangle, Incircle, Excircle, Collinear Tangency Points, Collinearity, Tutor

 

Recent Additions

Geometry Problems
Ten problems: 1401-1410
Visual Index
Open Problems
All Problems
Triangle
Circle
Incircle
Excircle
Tangent Line
Perpendicular lines
Collinear Points
View or Post a solution