Question 28
Let $ABC$ be a triangle with center of gravity $G$. Let $D \neq A$ be a point on the line $AG$ such that $AG = GD$, and $E \neq B$ is a point on the line $GB$ such that $GB = GE$. Finally, let $M$ be the midpoint of $AB$. Prove that the $BMC D$ quadrilateral is inscribed in a circumference if and only if $BA = BE$.