FI-MO 2010 Problem 5

Let $S$ be a non-empty subset of a plane. We say that the point $P$ can be seen from $A$ if every point from the line segment $AP$ belongs to $S$ . Further, the set $S$ can be seen from $A$ if every point of $S$ can be seen from $A$ . Suppose that $S$ can be seen from $A$ , $B$ and $C$ where $ABC$ is a triangle. Prove that $S$ can also be seen from any other point of the triangle $ABC$ .