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Ptolemy's Theorem yields as a corollary a pretty theorem [2] regarding an equilateral triangle inscribed in a circle. Given An equilateral triangle inscribed on a circle and a point on the circle. The distance from the point to the most distant vertex of the triangle is the sum of the distances from the point to the two nearer vertices.
For four points in order around a circle, Ptolemy's inequality becomes an equality, known as Ptolemy's theorem: ¯ ¯ + ¯ ¯ = ¯ ¯. In the inversion-based proof of Ptolemy's inequality, transforming four co-circular points by an inversion centered at one of them causes the other three to become collinear, so the triangle equality for these three points (from which Ptolemy's inequality may ...
In mathematics, Casey's theorem, also known as the generalized Ptolemy's theorem, is a theorem in Euclidean geometry named after the Irish mathematician John Casey. Formulation of the theorem [ edit ]
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Date/Time Thumbnail Dimensions User Comment; current: 20:05, 18 March 2008: 500 × 500 (5 KB): TheOtherJesse {{Information |Description=Diagram used in a proof of the Law of cosines using Ptolemy's theorem |Source=self-made, based on Ptolemy cos.jpg |Date=18 March 2008 |Author= TheOtherJesse |Permission= |other_versions=Ptolemy cos.jpg }}
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Special pages; Printable version; ... Diagram for geometric proof of en:Ptolemy's theorem ... distribute and/or modify this document under the terms of the GNU Free ...