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.