Question 36
Points $A$, $B$, $C$ in the plane satisfy $\overline{A B} = 2002$, $\overline{A C} = 9999$. The circles with diameters $A B$ and $A C$ intersect at $A$ and $D$. If $\overline{A D} = 37$, what is the shortest distance from point $A$ to line $B C$?