PL-OM 2011 Problem 2

The incircle of triangle $ABC$ is tangent to $BC,CA,AB$ at $D,E,F$ respectively. Consider the triangle formed by the line joining the midpoints of $AE,AF$ , the line joining the midpoints of $BF,BD$ , and the line joining the midpoints of $CD,CE$ . Prove that the circumcenter of this triangle coincides with the circumcenter of triangle $ABC$ .