Question 37
A semicircle with radius $2021$ has diameter $AB$ and center $O$. Points $C$ and $D$ lie on the semicircle such that $\angle AOC \lt \angle AOD = 90^\circ$. A circle of radius $r$ is inscribed in the sector bounded by $OA$ and $OC$ and is tangent to the semicircle at $E$. If $CD = CE$, compute $\lfloor r \rfloor$.