Incircle and excircles of a triangle polygon with any number of sides that has an inscribed circle—one that is tangent to each side—is called a tangential polygon. Incircle and excircles of a triangle In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of the incircle is a triangle center called the triangle's incenter. An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two. Every triangle has three
Orthocentroidal circle Orthocentroidal circle In geometry, the orthocentroidal circle of a non-equilateral triangle is the circle that has the triangle's orthocenter and its centroid at opposite ends of a diameter. This diameter also contains the triangle's nine-point center and is a subset of the Euler line, which also contains the circumcenter outside the orthocentroidal circle. Guinand showed in 1984 that the triangle's incenter must lie in the interior of the orthocentroidal circle, but not coinciding with the nine-point center; that is, it must fall in the open orthocentroidal disk punctured at the nine-point center. The incenter could be any such point, depending