Suppose $S$ is a convex figure in plane with area $10$. Consider a chord of length $3$ in $S$ and let $A$ and $B$ be two points on this chord which divide it into three equal parts. For a variable point $X$ in $S-\{A,B\}$, let $A'$ and $B'$ be the intersection points of rays $AX$ and $BX$ with the boundary of $S$. Let $S'$ be those points $X$ for which $AA'>\frac{1}{3} BB'$. Prove that the area of $S'$ is at least $6$. Proposed by Ali Khezeli