MEMO 2014 ekipno problem 6
Dodao/la:
arhivaSept. 24, 2014 Let the incircle

of the triangle

touch its side

at

. Let the line

intersect

at

and denote the excentre of

opposite to

by

. Let

and

be the midpoints of

and

respectively.
Prove that the points

,

,

, and

are concyclic.
%V0
Let the incircle $k$ of the triangle $ABC$ touch its side $BC$ at $D$. Let the line $AD$ intersect $k$ at $L \neq D$ and denote the excentre of $ABC$ opposite to $A$ by $K$. Let $M$ and $N$ be the midpoints of $BC$ and $KM$ respectively.
Prove that the points $B$, $C$, $N$, and $L$ are concyclic.
Source: Srednjoeuropska matematička olimpijada 2014, ekipno natjecanje, problem 6