Problem 323: Triangle, Incenter, Circumcenter, Equal circles, Collinearity.
Level: High School, College, SAT Prep.

The figure shows a triangle ABC with incenter I and circumcenter O. Circles D, E, and F are congruent circles passing through point G. Circle D is tangent to AB and AC, circle E is tangent to AB and BC, and circle F is tangent to AC and BC. Prove that O, G, and I are collinear.