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Due to the Pythagorean theorem the number () has the simple geometric meanings shown in the diagram: For a point outside the circle () is the squared tangential distance | | of point to the circle . Points with equal power, isolines of Π ( P ) {\displaystyle \Pi (P)} , are circles concentric to circle c {\displaystyle c} .
In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid's Elements. [1]
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 ...
Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem.
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). The theorem is named for Leonhard Euler, who published it ...
Each circle is labeled by an integer i, its position in the sequence; it has radius ρ i and curvature ρ −i. When the four radii of the circles in Descartes' theorem are assumed to be in a geometric progression with ratio , the curvatures are also in the same progression (in reverse). Plugging this ratio into the theorem gives the equation
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 ...
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 ...