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A polygon inscribed in a circle is said to be a cyclic polygon, and the circle is said to be its circumscribed circle or circumcircle. The inradius or filling radius of a given outer figure is the radius of the inscribed circle or sphere, if it exists.
This circle is called the incircle of the quadrilateral or its inscribed circle, its center is the incenter and its radius is called the inradius. Since these quadrilaterals can be drawn surrounding or circumscribing their incircles, they have also been called circumscribable quadrilaterals , circumscribing quadrilaterals , and circumscriptible ...
In geometry, a circumscribed circle for a set of points is a circle passing through each of them. Such a circle is said to circumscribe the points or a polygon formed from them; such a polygon is said to be inscribed in the circle. Circumcircle, the circumscribed circle of a triangle, which always exists for a given triangle.
Ex-tangential quadrilateral – Convex 4-sided polygon whose sidelines are all tangent to an outside circle; Harcourt's theorem – Area of a triangle from its sides and vertex distances to any line tangent to its incircle; Incenter–excenter lemma – A statement about properties of inscribed and circumscribed circles
In geometry, Euler's theorem states that the distance d between the circumcenter and incenter of a triangle is given by [1] [2] = or equivalently + + =, where and denote the circumradius and inradius respectively (the radii of the circumscribed circle and inscribed circle respectively).
In geometry, the circumscribed circle or circumcircle of a triangle is a circle that passes through all three vertices. The center of this circle is called the circumcenter of the triangle, and its radius is called the circumradius .
Examples of cyclic quadrilaterals. In Euclidean geometry, a cyclic quadrilateral (a.k.a. concyclic quadrilateral, inscribed quadrilateral), is a quadrilateral (four-sided figure) whose four vertices are concyclic (all lying on a single enclosing circle, called the circumcircle).
In Euclidean geometry, a tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within the trapezoid: the incircle or inscribed circle. It is the special case of a tangential quadrilateral in which at least one pair of opposite sides are parallel.