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The chain closes, in the sense that the sixth circle is always tangent to the first circle. [1] [2] It is assumed in this construction that all circles lie within the triangle, and all points of tangency lie on the sides of the triangle. If the problem is generalized to allow circles that may not be within the triangle, and points of tangency ...
Seven circles theorem – A chain of six circles tangent to a seventh circle and each to its 2 neighbors; Six circles theorem – Relates to a chain of six circles together with a triangle; Smallest circle problem – Finding the smallest circle that contains all given points; Tammes problem – Circle packing problem
Another proof that uses triangles considers the area enclosed by a circle to be made up of an infinite number of triangles (i.e. the triangles each have an angle of d๐ at the center of the circle), each with an area of โ 1 / 2 โ · r 2 · d๐ (derived from the expression for the area of a triangle: โ 1 / 2 โ · a · b · sin๐ ...
Print/export Download as PDF ... This category has the following 2 subcategories, out of 2 total. ... Pages in category "Theorems about circles" The following 21 ...
The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. 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, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
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