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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 ...
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, 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.
Familiar examples of inscribed figures include circles inscribed in triangles or regular polygons, and triangles or regular polygons inscribed in circles. A circle inscribed in any polygon is called its incircle, in which case the polygon is said to be a tangential polygon. A polygon inscribed in a circle is said to be a cyclic polygon, and the ...
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 .
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).
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).
This is the triangular case of Poncelet's closure theorem, which applies more generally to polygons of any number of sides and to conics other than circles. It is the first known mathematical publication on pairs of inscribed and circumscribed circles of polygons, and significantly predates Poncelet's own 1822 work in this area. [3]