Question 84
Let $D$ be the point different from $B$ on the hypotenuse $AB$ of a right triangle $ABC$ such that $|CB| = |CD|$. Let $O$ be the circumcenter of triangle $ACD$. Rays $OD$ and $CB$ intersect at point $P$, and the line through point $O$ perpendicular to side $AB$ and ray $CD$ intersect at point $Q$. Points $A$, $C$, $P$, $Q$ are concyclic. Does this imply that $ACPQ$ is a square?