The figure below show a triangle ABC
with the circumcircle O. Circle OC passing through A an B is tangent
to BC at B. Circle OA passing through B and C is tangent to AB
at B. Circles OA and OC 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.