Geometry Problem 1410: Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle

Proposition

The figure below shows a right triangle ABC (angle B = 90 degree) with the incircle I tangent to BC at D. The excircle E corresponding to BC is tangent to AB and AC extended at F and G, respectively. Prove that the measure of the angle DBG is 45 degree.
 
 

Geometry Problem 1410: Right Triangle, Incircle, Excircle, Tangency Points, 45 Degree Angle, Tutor

 

Poster of Problem 1410: Sketching, iPad, Typography, Art

Poster of Geometry Problem 1410: Right Triangle, Incircle, Excircle, Tangency Points, Sketching, iPad, Typography, Art, SW, Tutor

 

See also: Typography and poster of problem 1408.