BALKAN 2004 Problem 3

Let $O$ be an interior point of an acute triangle $ABC$ . The circles with centers the midpoints of its sides and passing through $O$ mutually intersect the second time at the points $K$ , $L$ and $M$ different from $O$ . Prove that $O$ is the incenter of the triangle $KLM$ if and only if $O$ is the circumcenter of the triangle $ABC$ .