MathDB

Let

K

and

L

be the centers of the excircles of a non-isosceles triangle

ABC

opposite

B

and

C

respectively. Let

M

and

N

be points in the plane of the triangle such that

BM

bisects

AC

and

CN

bisects

AB

. Prove that the lines

KM

and

NK

meet on

BC

.
The problem in its current formulation is trivially wrong. No possible rectification is known to OP / was sent to the participants.

Problem Statement