Question 139
Let $ABCD$ be a convex quadrilateral inscribed in a circle with shortest side $AB$. The ratio $[BCD]/[ABD]$ is an integer (where $[XYZ]$ denotes the area of triangle $XYZ$.) If the lengths of $AB$, $BC$, $CD$, and $DA$ are distinct integers no greater than $10$, find the largest possible value of $AB$.