Question 29
Let $ABCD$ be a quadrilateral inscribed in the circle $c(O, R)$ and let $K, L, M, N, S, T$ be the midpoints of the segments $AB, BC, CD, AD, AC$ and $BD$, respectively. Prove that the centers of the circumcircles of the triangles $KLS, LMT, MNS$ and $NKT$ form a cyclic quadrilateral similar to $ABCD$.