BALKAN-SL 2012 G3

Let $ABC$ be a triangle with circumcircle $c$ and circumcenter $O$ , and let $D$ be a point on the side $BC$ different from the vertices and the midpoint of $BC$ . Let $K$ be the point where the circumcircle $c_1$ of the triangle $BOD$ intersects $c$ for the second time and let $Z$ be the point where $c_1$ meets the line $AB$ . Let $M$ be the point where the circumcircle $c_2$ of the triangle $COD$ intersects $c$ for the second time and let $E$ be the point where $c_2$ meets the line $AC$ . Finally let $N$ be the point where the circumcircle $c_3$ of the triangle $AEZ$ meets $c$ again. Prove that the triangles $ABC$ and $NKM$ are congruent.