MathNet 2011 Question 6

Let $O$ be the center of rectangle $ABCD$, and let $K$ lie on its circumcircle. Line $CK$ intersects segment $AD$ at $M$, with $AM:MD=2$. Prove that the centroid of triangle $OKD$ lies on the circumcircle of triangle $COD$. (V. Shmarov)