Problem #WSP-5302

Problem

Let $ABC$ be a triangle with midpoints $D$ on the side $BC$, $E$ on the side $AC$, and $F$ on the side $AB$. Let $M$ be the point of intersection of all medians of the triangle $ABC$, let $H$ be the point of intersection of the heights $AJ$, $BI$ and $CK$. Prove that the points $D,J,I,E,F,K$ lie on one circle. What can you say about the center of that circle?