Question 3
Let $ABC$ be a triangle with $AB = 5$, $BC = 6$, $CA = 7$. Let $D$ be a point on ray $AB$ beyond $B$ such that $BD = 7$, $E$ be a point on ray $BC$ beyond $C$ such that $CE = 5$, and $F$ be a point on ray $CA$ beyond $A$ such that $AF = 6$. Compute the area of the circumcircle of $DEF$.