MathDB

In triangle

ABC

let

F

denote the midpoint of side

BC

. Let the circle passing through point

A

and tangent to side

BC

at point

F

intersect sides

AB

and

AC

at points

M

and

N

, respectively. Let the line segments

CM

and

BN

intersect in point

X

. Let

P

be the second point of intersection of the circumcircles of triangles

BMX

and

CNX

. Prove that points

A, F

and

P

are collinear.
Proposed by Imolay András, Budapest

Problem Statement