Problem 589: Triangle, Incenter, Incircle, Tangency Point, Midpoint,
Perpendicular, Distance. Level: Mathematics Education, High School, College

The figure shows a triangle ABC.
The incircle O is tangent to AC at D. M is the midpoint of AC. Line AE
is perpendicular to BO extended. Prove
that the measure of DM is equal to half the measure of CE.