Question 111
In triangle $ABC$, $AB = 6$, $BC = 7$ and $CA = 8$. Let $D$, $E$, $F$ be the midpoints of sides $BC$, $AC$, $AB$, respectively. Also let $O_{A}$, $O_{B}$, $O_{C}$ be the circumcenters of triangles $AFD$, $BDE$, and $CEF$, respectively. Find the area of triangle $O_{A} O_{B} O_{C}$.