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Download QR code; Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. ... Clifford's circle theorems; Constant chord theorem; D.
Conway's circle theorem as a special case of the generalisation, called "side divider theorem" (Villiers) or "windscreen wiper theorem" (Polster)) Conway's circle is a special case of a more general circle for a triangle that can be obtained as follows: Given any ABC with an arbitrary point P on line AB.
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,
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.
A very short proof of this theorem based on Casey's theorem on the bitangents of four circles tangent to a fifth circle was published by John Casey in 1866; [5] Feuerbach's theorem has also been used as a test case for automated theorem proving. [6] The three points of tangency with the excircles form the Feuerbach triangle of the given triangle.
For a circle, the width is the same as the diameter; a circle of width w has perimeter π w. A Reuleaux triangle of width w consists of three arcs of circles of radius w. Each of these arcs has central angle π /3, so the perimeter of the Reuleaux triangle of width w is equal to half the perimeter of a circle of radius w and therefore is equal ...
In Euclidean geometry, Kosnita's theorem is a property of certain circles associated with an arbitrary triangle. Let A B C {\displaystyle ABC} be an arbitrary triangle, O {\displaystyle O} its circumcenter and O a , O b , O c {\displaystyle O_{a},O_{b},O_{c}} are the circumcenters of three triangles O B C {\displaystyle OBC} , O C A ...
The integral of ds over the whole circle is just the arc length, which is its circumference, so this shows that the area A enclosed by the circle is equal to / times the circumference of the circle. 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 ...