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
Polar circle (geometry) Polar circle (geometry) In geometry, the polar circle of a triangle is the circle whose center is the triangle's orthocenter and whose squared radius is where "A, B, C" denote both the triangle's vertices and the angle measures at those vertices, "H" is the orthocenter (the intersection of the triangle's altitudes), "D", "E", "F" are the feet of the altitudes from vertices "A, B, C" respectively, "R" is the triangle's circumradius (the radius of its circumscribed circle), and "a", "b", "c" are the lengths of the triangle's sides opposite vertices "A", "B", "C" respectively. The first parts of the radius