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The Eight circles theorem and its dual can degenerate into Brianchon's theorem and Pascal's theorem when the conic in these theorems is a circle. Specifically: When circle () degenerates into a point, the Eight circles theorem degenerates into Brianchon's theorem [7] [9]. When circle () degenerates into a point and moves to infinity, the dual ...
Download as PDF; Printable version; In other projects Wikidata item; ... Pages in category "Theorems about circles" The following 21 pages are in this category, out ...
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 ...
Download as PDF; Printable version; In other projects ... Pages in category "Theorems about triangles and circles" The following 18 pages are in this category, out of ...
This problem is known as the primitive circle problem, as it involves searching for primitive solutions to the original circle problem. [9] It can be intuitively understood as the question of how many trees within a distance of r are visible in the Euclid's orchard , standing in the origin.
Download as PDF; Printable version; ... Pages in category "Theorems about quadrilaterals and circles" The following 6 pages are in this category, out of 6 total ...