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where r is the inradius and R is the circumradius of the triangle. Here the sign of the distances is taken to be negative if and only if the open line segment DX (X = F, G, H) lies completely outside the triangle. In the diagram, DF is negative and both DG and DH are positive. The theorem is named after Lazare Carnot (1753–1823).
Radius of gyration, the root-mean-square distance from a set of points or masses to a given center; The radial coordinate in a Polar coordinate system (2D) Cylindrical coordinate system (3D) Spherical coordinate system (3D) The inradius or circumradius of a shape
Carnot's theorem (inradius, circumradius), describing a property of the incircle and the circumcircle of a triangle; Carnot's theorem (conics), describing a relation between triangles and conic sections; Carnot's theorem (perpendiculars), describing a property of certain perpendiculars on triangle sides; In physics:
The incircle is the circle that lies inside the triangle and touches all three sides. Its radius is called the inradius. There are three other important circles, the excircles; they lie outside the triangle and touch one side, as well as the extensions of the other two. The centers of the incircles and excircles form an orthocentric system. [26]
A tangential quadrilateral with its incircle. In Euclidean geometry, a tangential quadrilateral (sometimes just tangent quadrilateral) or circumscribed quadrilateral is a convex quadrilateral whose sides all can be tangent to a single circle within the quadrilateral.
If r and R are the inradius and the circumradius respectively, then the area K satisfies the inequalities [14]. There is equality on either side only if the quadrilateral is a square. Another inequality for the area is [15]: p.39, #1203
U.S. President Donald Trump will take part virtually in the World Economic Forum's annual meeting in Davos just days after his inauguration, the forum president said Tuesday. Børge Brende, a ...
The radius of the sphere inscribed in a polyhedron P is called the inradius of P. Interpretations. All regular polyhedra have inscribed spheres, ...