Question 24
Circles centered at $A$ and $B$ each have radius $2,$ as shown. Point $O$ is the midpoint of $\overline{AB},$ and $OA = 2\sqrt{2}.$ Segments $OC$ and $OD$ are tangent to the circles centered at $A$ and $B,$ respectively, and $\overline{EF}$ is a common tangent. What is the area of the shaded region $ECODF?$
