MathDB

Let

ABC

be a triangle with

AB < AC

and let

D{}

be the other intersection point of the angle bisector of

\angle A

with the circumcircle of the triangle

ABC

. Let

E{}

and

F{}

be points on the sides

AB

and

AC

respectively, such that

AE = AF

and let

P{}

be the point of intersection of

AD

and

EF

. Let

M{}

be the midpoint of

BC{}

. Prove that

AM

and the circumcircles of the triangles

AEF

and

PMD

pass through a common point.

Problem Statement