Two circles ...
Source: INMO 1996 Problem 2
October 6, 2005
geometryinequalitiesanalytic geometryvectorcircumcirclefunctiontrigonometry
Problem Statement
Let and be two concentric circles in the plane with radii and respectively. Show that the orthocenter of any triangle inscribed in circle lies in the interior of circle . Conversely, show that every point in the interior of is the orthocenter of some triangle inscribed in .