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Circle through exactly four points given by Schinzel's construction Schinzel proved this theorem by the following construction. If n {\displaystyle n} is an even number, with n = 2 k {\displaystyle n=2k} , then the circle given by the following equation passes through exactly n {\displaystyle n} points: [ 1 ] [ 2 ] ( x − 1 2 ) 2 + y 2 = 1 4 5 ...
As stated above, Thales's theorem is a special case of the inscribed angle theorem (the proof of which is quite similar to the first proof of Thales's theorem given above): Given three points A, B and C on a circle with center O, the angle ∠ AOC is twice as large as the angle ∠ ABC. A related result to Thales's theorem is the following:
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
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.
Download QR code; Print/export Download as PDF; ... Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total.
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} .
The following proof is attributable [2] to Zacharias. [3] Denote the radius of circle by and its tangency point with the circle by . We will use the notation , for the centers of the circles. Note that from Pythagorean theorem,
This is known as the six circles theorem. [10] It is also known as the four circles theorem and while generally attributed to Jakob Steiner the only known published proof was given by Miquel. [11] David G. Wells refers to this as Miquel's theorem. [12]