Problem 361. Right triangle, Incircle, Incenter, Tangency points, Angle.
Level: High School, College, SAT Prep.

The figure shows a right triangle ABC with incircle O and points of tangency D and E. If CO intersects DE at F, prove that the measure of angle CFE is 45 degrees.
 

 

The incircle or inscribed circle of a triangle touches (is tangent to) the three sides. The center of the incircle is called the incenter.