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.