Online Geometry Problem 713: Tangent Circles, Diameter, Chord, Tangent,
Incenter, Incircle, Triangle.
Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows the circles O and O' tangent at
B. AB is the diameter of circle O, AC is tangent to circle O' at
D, AE is tangent to circle O' at F, and DF meets AB at I. Prove that I
is the incenter of triangle ACE.