Let C1 and C2 be two concentric circles in the plane with radii R and 3R respectively. Show that the orthocenter of any triangle inscribed in circle C1 lies in the interior of circle C2. Conversely, show that every point in the interior of C2 is the orthocenter of some triangle inscribed in C1. geometryinequalitiesanalytic geometryvectorcircumcirclefunctiontrigonometry