Geometry Problem 1269

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

In a triangle ABC, the inscribed circle of center O is tangent to the sides at D, E, and F, as shown in the figure. AO extended meets DE at A1. Prove that angle AA1C = 90 degrees.


Geometry Problem 1269: Triangle, Incircle, Incenter, Inscribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector