MathDB

Let

A,B,C,D

and

E

be five points lying in this order on a circle, such that

AD=BC

. The lines

AD

and

BC

meet at a point

F

. The circumcircles of the triangles

CEF

and

ABF

meet again at the point

P

.
Prove that the circumcircles of triangles

BDF

and

BEP

are tangent to each other.

Problem Statement