MEMO 2014 ekipno problem 6


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24. rujna 2014.
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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.
Izvor: Srednjoeuropska matematička olimpijada 2014, ekipno natjecanje, problem 6