Question 66
Let $PMO$ be a triangle with $PM = 2$ and $\angle PMO = 120^\circ$. Let $B$ be a point on $PO$ such that $PM$ is perpendicular to $MB$, and suppose that $PM = BO$. The product of the lengths of the sides of the triangle can be expressed in the form $a + b \sqrt[3]{c}$, where $a, b, c$ are positive integers, and $c$ is minimized. Find $a + b + c$.