MathNet 2010 — Part 07 Question 150

Let $O$ be the point $(0,0)$. Let $A$, $B$, $C$ be three points in the plane such that $A O = 15$, $B O = 15$, and $C O = 7$, and such that the area of triangle $A B C$ is maximal. What is the length of the shortest side of $A B C$?