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
Hyperbolic geometry of a circle of radius "r" is equal to: And the area of the enclosed disk is: Therefore, in hyperbolic geometry the ratio of a circle's circumference to its radius is always strictly greater than formula_7, though it can be made arbitrarily close by selecting a small enough circle. If the Gaussian curvature of the plane is −1 then the geodesic curvature of a circle of radius "r" is: formula_8 In hyperbolic geometry, there is no line that remains equidistant from another. Instead, the points that all have the same orthogonal distance from a given line lie on a curve