Question 1
Let $\Omega$ be a circle of radius $8$ centered at point $O$, and let $M$ be a point on $\Omega$. Let $S$ be the set of points $P$ such that $P$ is contained within $\Omega$, or such that there exists some rectangle $ABCD$ containing $P$ whose center is on $\Omega$ with $AB=4$, $BC=5$, and $BC \parallel OM$. Find the area of $S$.