Question 26
Semicircle $\overset{\frown}{AB}$ has center $C$ and radius $1.$ Point $D$ is on $\overset{\frown}{AB}$ and $CD\perp AB.$ Extend $\overline{BD}$ and $\overline{AD}$ to $E$ and $F,$ respectively, so that circular arcs $\overset{\frown}{AE}$ and $\overset{\frown}{BF}$ have $B$ and $A$ as their respective centers. Circular arc $\overset{\frown}{EF}$ has center $D.$ The area of the shaded “smile,” $AEFBDA,$ is
