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
Dividing a circle into areas Dividing a circle into areas In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with "n" sides, in such a way as to "maximise" the number of areas created by the edges and diagonals, has a solution by an inductive method. If we already have "n" points on the circle and add one more point, we draw "n" lines from the new point to previously existing points. Two cases are possible. In the first case (a), the new line passes through a point where two or more old lines (between previously existing points)