Geometry Problem 937: Triangle, Circumcircle, Circles, Tangent, Sides, Midpoint. Level: High School, College, Mathematics Education

The figure below show a triangle ABC with the circumcircle O. Circle O_C passing through A an B is tangent to BC at B. Circle O_A passing through B and C is tangent to AB at B. Circles O_A and O_C intersect at B and D. BD extended meets the circumcircle O at E. Prove that D is the midpoint of BE. This entry contributed by Ajit Athle.