MathDB

In a non-isosceles triangle

ABC

the centre of the incircle is denoted by

I

. The other intersection point of the angle bisector of

\angle BAC

and the circumcircle of

\vartriangle ABC

D

. The line through

I

perpendicular to

AD

intersects

BC

F

. The midpoint of the circle arc

BC

on which

A

lies, is denoted by

M

. The other intersection point of the line

MI

and the circle through

B, I

and

C

, is denoted by

N

. Prove that

FN

is tangent to the circle through

B, I

and

C

Problem Statement