MathDB

Let

\triangle ABC

be a triangle with incentre

I

. Points

E

and

F

are the tangency points of the incircle and the sides

AC

and

AB

, respectively. Suppose that the lines

BI

and

CI

intersect the line

EF

Y

and

Z

, respectively. Let

M

denote the midpoint of the segment

BC

, and

N

denote the midpoint of the segment

YZ

. Prove that

AI \parallel MN

Problem Statement