MathDB

In scalene triangle

ABC

the shortest side is

BC

. Let points

M

and

N

be chosen on sides

AB

and

AC

, respectively, such that

BM=CN=BC

. Let

I

and

O

denote the incenter and circumcentre of triangle

ABC

, and let

D

and

E

denote the incenter and circumcenter of triangle

AMN

. Prove that lines

IO

and

DE

intersect each other on the circumcircle of triangle

ABC

.
Submitted by Luu Dong, Vietnam

Problem Statement