5. [4] Circle $B$ has radius $6 \sqrt{7}$. Circle $A$, centered at point $C$, has radius $\sqrt{7}$ and is contained in $B$. Let $L$ be the locus of centers $C$ such that there exists a point $D$ on the boundary of $B$ with the following property: if the tangents from $D$ to circle $A$ intersect circle $B$ again at $X$ and $Y$, then $X Y$ is also tangent to $A$. Find the area contained by the boundary of $L$.
Answer: $168 \pi$
Solution: The conditions imply that there exists a triangle such that $B$ is the circumcircle and $A$ is the incircle for the position of $A$. The distance between the circumcenter and incenter is given by $\sqrt{(R-2 r) R}$, where $R, r$ are the circumradius and inradius, respectively. Thus the locus of $C$ is a circle concentric to $B$ with radius $2 \sqrt{42}$. The conclusion follows.