21. On a sphere with a diameter of 1, there are three points $A$, $B$, and $C$. If the spherical distances between $A$ and $B$, and between $A$ and $C$ are both $\frac{\pi}{3}$,

and the spherical distance between $B$ and $C$ is $\frac{\pi}{2}$, then the distance of the plane section $A B C$ through the center of the sphere is . $\qquad$
21. $\frac{\sqrt{2}}{2}$