Online Geometry Problem 454: Triangle, Incircle, Inradius, Tangent, Circle, Radius, Radii. Level: High School, Honors Geometry, College, Mathematics Education

The figure shows a triangle ABC with the incircle O of radius r. Circle O intersects OA, OB and OC at D, E, and F, respectively. If r_a, r_b, and r_c, are the radii of circles tangent to the sides and to the incircle O at D, E, and F, respectively, prove that .