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eyeball theorem, red chords are of equal length theorem variation, blue chords are of equal length. The eyeball theorem is a statement in elementary geometry about a property of a pair of disjoined circles. More precisely it states the following: [1]
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
In plane geometry, the Conway circle theorem states that when the sides meeting at each vertex of a triangle are extended by the length of the opposite side, the six endpoints of the three resulting line segments lie on a circle whose centre is the incentre of the triangle.
Secant-, chord-theorem. For the intersecting secants theorem and chord theorem the power of a point plays the role of an invariant: . Intersecting secants theorem: For a point outside a circle and the intersection points , of a secant line with the following statement is true: | | | | = (), hence the product is independent of line .
Pages in category "Theorems about circles" The following 21 pages are in this category, out of 21 total. This list may not reflect recent changes. B. Butterfly ...
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 ...
The circle packing theorem was first proved by Paul Koebe. [17] William Thurston [1] rediscovered the circle packing theorem, and noted that it followed from the work of E. M. Andreev. Thurston also proposed a scheme for using the circle packing theorem to obtain a homeomorphism of a simply connected proper subset of the plane onto the interior ...
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 ...
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