Question 191
Convex quadrilateral $BCDE$ lies in the plane. Lines $EB$ and $DC$ intersect at $A$, with $AB = 2$, $AC = 5$, $AD = 200$, $AE = 500$, and $\cos \angle BAC = \frac{7}{9}$. What is the largest number of nonoverlapping circles that can lie in quadrilateral $BCDE$ such that all of them are tangent to both lines $BE$ and $CD$?