Problem 591: Triangle, Incenter, Incircle, Inradius, Tangency Point, Midpoint, Altitude, Congruence. Level: Mathematics Education, High School, College

The figure shows a triangle ABC with the incircle O tangent to AC at D. M is the midpoint of AC and BE is the altitude. If BE and MO extended meet at F, prove that BF is equal to the inradius of triangle ABC.