HMMT 2021 U3

A semicircle with radius 2021 has diameter $A B$ and center $O$. Points $C$ and $D$ lie on the semicircle such that $\angle A O C<\angle A O D=90^{\circ}$. A circle of radius $r$ is inscribed in the sector bounded by $O A$ and $O C$ and is tangent to the semicircle at $E$. If $C D=C E$, compute $\lfloor r\rfloor$.