Question 45
Alice has an equilateral triangle $A B C$ of area $1$. Put $D$ on $B C$, $E$ on $C A$, and $F$ on $A B$, with $B D = D C$, $C E = 2 E A$, and $2 A F = F B$. Note that $A D$, $B E$, and $C F$ pass through a single point $M$. What is the area of triangle $E M C$?