Question 173
Let $\Gamma$ be the circumcircle of triangle $ABC$. Let $A'$ be the mid-point of arc $BC$ of the circle $\Gamma$ opposite to $A$, $B'$ be the mid-point of arc $CA$ opposite to $B$ and $C'$ be the mid-point of arc $AB$ opposite to $C$. If the area of the triangle $AB'C'$, $A'BC'$, $A'B'C$ is $2$, $3$, $4$, respectively, what is the area of triangle $ABC$?