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Fairly standard configuration involving tangents

Source: MEMO 2017 T6

August 25, 2017

geometry

Problem Statement

Let

ABC

be an acute-angled triangle with

AB \neq AC

, circumcentre

O

and circumcircle

\Gamma

. Let the tangents to

\Gamma

at

B

and

C

meet each other at

\Gamma

, and let the line

N \neq A

intersect

BC

at

E

. Denote the midpoint of

BC

by

M

and let

AM

meet

\Gamma

again at

N \neq A

. Finally, let

F \neq A

be a point on

\Gamma

such that

A, M, E

and

F

are concyclic. Prove that

FN

bisects the segment

MD

.

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