Geometry Problem 1270

Elements: Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector

In a triangle ABC, the excircle or escribed circle of center O relative to AC is tangent to the sides at D, E, and F, as shown in the figure. CO cuts DE at C1. Prove that angle AC1C = 90 degrees.


Geometry Problem 1270: Triangle, Excircle, Excenter, Escribed Circle, Tangency Points, Perpendicular, 90 Degrees, Angle Bisector