Question 85
Let $D$ be the midpoint of the side $BC$, $E$ the midpoint of the side $CA$ and $T$ the center of mass of a triangle $ABC$. Let the lines $AT$, $BT$ and $CT$ also intersect the circumcircle of the triangle $ABC$ at the points $P$, $Q$ and $R$, respectively. Suppose $\angle ACB = \angle RQP$. Prove that $DCET$ is a cyclic quadrilateral.