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.