Question 174
Let $\triangle ABC$ be a triangle. $M$ is the midpoint of $AC$, $D$ is a point on $AB$. $BM$ and $CD$ meet at $O$, with $AB = CO$. $E$ is a point on $AC$ such that $DE // BM$. Prove that $AB \perp BC$ if and only if $ADOM$ is a cyclic quadrilateral.