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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.
English: Animated visual proof of Ptolemy's theorem, based on W. Derrick, J. Herstein (2012) Proof Without Words: Ptolemy's Theorem, The College Mathematics Journal, v 43, n 5, p 386 Date 22 May 2022
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 ...
Season 3 Episode 13: "Video Game Release" (2018) – A new video game is released in Cloud 9. Tiny Toons Looniversity. Season 2 Episode 3: "Tooned In Space" (2024) – Sweetie is obsessed with her game console. Todd and the Book of Pure Evil. Season 2 Episode 6: "Fisting Fantasy" (2011) – Todd and his friends are trapped in a video game ...
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 ]
Ryan Reynolds’ Maximum Effort and Fubo have ordered new original series “Neon Dimension,” a video game show hosted by actor and comedian Flula Borg, for their Maximum Effort Channel. More ...
Fox on Thursday revealed the full cast for its upcoming reality series Stars on Mars, featuring 12 contestants who will attempt to become the last space invader standing. According to the official ...
Proof of law of cosines using Ptolemy's theorem. Referring to the diagram, triangle ABC with sides AB = c, BC = a and AC = b is drawn inside its circumcircle as shown. Triangle ABD is constructed congruent to triangle ABC with AD = BC and BD = AC. Perpendiculars from D and C meet base AB at E and F respectively.