Geometry Problem 1265

Elements: Triangle, Incircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector

Given a triangle ABC. Let D, E, and F be the points of tangency of the incircle, as shown in the figure. If FG is perpendicular to DE (G on DE), prove that GF is the bisector of angle AGC.


Geometry Problem 1265: Triangle, Incircle, Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector