-gon equals the product of the perpendicular distances from to the sides of the second -gon. Point on the circumcircle Let a cyclic -gon have vertices on the unit circle. Then for any point on the minor arc , the distances from to the vertices satisfy For a regular -gon, if are the distances from any point on the circumcircle to the vertices , then Polygon circumscribing constant Any regular polygon is cyclic. Consider a unit circle, then circumscribe a regular triangle such that each side touches the circle. Circumscribe a circle, then circumscribe a square. Again circumscribe a circle, then circumscribe a regular pentagon, and so on. The radii of the circumscribed circles converge to the so-called polygon circumscribing constant . The reciprocal of this constant is the Kepler–Bouwkamp constant. See also Circumcenter of mass Circumgon Circumscribed sphere Circumcevian triangle Inscribed circle Japanese theorem for cyclic polygons Japanese theorem for cyclic quadrilaterals Jung's theorem, an inequality relating the diameter of a point set to the radius of its minimum bounding sphere Kosnita theorem Lester's theorem Tangential polygon Triangle center References External links Derivation of formula for radius of circumcircle of triangle at Mathalino.com Semi-regular angle-gons and side-gons: respective generalizations of rectangles and rhombi at Dynamic Geometry Sketches, interactive dynamic geometry sketch. MathWorld Interactive Triangle circumcircle and circumcenter With interactive animation An interactive Java applet for the circumcenter Circles defined for a triangle Compass and straightedge constructions