INMO 1996 Problem 2

Let $C_1$ and $C_2$ be two concentric circles in the plane with radii $R$ and $3R$ respectively. Show that the orthocenter of any triangle inscribed in circle $C_1$ lies in the interior of circle $C_2$ . Conversely, show that every point in the interior of $C_2$ is the orthocenter of some triangle inscribed in $C_1$ .