To prove orthocenter of triangle inscribed incircle of radius r lies in cocentric circle of radius 3r

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

• Have you tried anything? Please edit to show so. – Gerard L. Nov 8 '17 at 12:36
• – Martin Sleziak Nov 8 '17 at 13:32
• @MartinSleziak: Indeed, but not quite a duplicate because the other question lacks the converse. – Alex M. Nov 8 '17 at 13:35