MathDB

Let

I{}

be the incircle of the triangle

ABC

. Let

A_1, B_1

and

C_1

be the midpoints of the sides

BC, CA

and

AB

respectively. The point

X{}

is symmetric to

I{}

with respect to

A_1

. The line

\ell

parallel to

BC

and passing through

X{}

intersects the lines

A_1B_1

and

A_1C_1

M{}

and

N{}

respectively. Prove that one of the excenters of the triangle

ABC

lies on the

A_1

-excircle of the triangle

A_1MN

Problem Statement