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Geometry |
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Authors: Harish Chandra Rajpoot
In this paper, the generalized formula have been derived to analytically compute the radii of the circles inscribed and circumscribed by three mutually tangent circles of known radii. The formulation and analysis of three external tangent circles packed in the smallest rectangle and the intersection circles have also been done. . The analytic formula derived here can also be used in case of three tangent spheres in three dimensions. These formula are also used for calculating any of three radii if rest two are known & computing the length of common chord, angle of intersection & area of intersection of two intersecting circles. The generalized formula derived here can also be used to derive the recurrence relations for circle packing over a plane which can further be extended into 3 dimensions for sphere packings.
Comments: 14 Pages, 6 Figures
Download: PDF
[v1] 2026-02-06 00:17:57
Unique-IP document downloads: 107 times
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