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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
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.
Diagram for geometric proof of en:Ptolemy's theorem. ... distribute and/or modify this document under the terms of the GNU Free Documentation License, ...
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 ...
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 }}
Women in six U.S. states are now effectively allowed to be topless in public, according to a new ruling by the U.S. 10th Circuit Court of Appeals. 'Free the Nipple' movement: Women can now legally ...
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. Then:
“I saw three toes that were forming, and now there’s length to them tonight,” the woman claimed. “I can stand on my tippy-toes!” Woman’s toes grew back because of prayer, Missouri ...