Question 39
Equilateral triangle $A B C$ has circumcircle $\Omega$. Points $D$ and $E$ are chosen on minor arcs $A B$ and $A C$ of $\Omega$ respectively such that $B C = D E$. Given that triangle $A B E$ has area $3$ and triangle $A C D$ has area $4$, find the area of triangle $A B C$.