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Brahmagupta theorem: Difference between revisions
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[[Image:Brahmaguptra's theorem.svg|thumb|<math> \overline{ | [[Image:Brahmaguptra's theorem.svg|thumb|<math> \overline{BM}\perp\overline{AC},\overline{EF}\perp\overline{BC} </math> <math>\Rightarrow |\overline{AF}|=|\overline{FD}| </math>]] | ||
In [[geometry]], '''Brahmagupta's theorem''' states that if a [[cyclic quadrilateral]] is [[Orthodiagonal quadrilateral|orthodiagonal]] (that is, has [[perpendicular]] [[diagonals]]), then the perpendicular to a side from the point of intersection of the diagonals always [[Bisection|bisects]] the opposite side.<ref>Michael John Bradley (2006). ''The Birth of Mathematics: Ancient Times to 1300''. Publisher Infobase Publishing. {{ISBN|0816054231}}. Page 70, 85.</ref> It is named after the [[List of Indian mathematicians|Indian mathematician]] [[Brahmagupta]] (598-668).<ref>[[Harold Scott MacDonald Coxeter|Coxeter, H. S. M.]]; Greitzer, S. L.: ''Geometry Revisited''. Washington, DC: Math. Assoc. Amer., p. 59, 1967</ref> | In [[geometry]], '''Brahmagupta's theorem''' states that if a [[cyclic quadrilateral]] is [[Orthodiagonal quadrilateral|orthodiagonal]] (that is, has [[perpendicular]] [[diagonals]]), then the perpendicular to a side from the point of intersection of the diagonals always [[Bisection|bisects]] the opposite side.<ref>Michael John Bradley (2006). ''The Birth of Mathematics: Ancient Times to 1300''. Publisher Infobase Publishing. {{ISBN|0816054231}}. Page 70, 85.</ref> It is named after the [[List of Indian mathematicians|Indian mathematician]] [[Brahmagupta]] (598-668).<ref>[[Harold Scott MacDonald Coxeter|Coxeter, H. S. M.]]; Greitzer, S. L.: ''Geometry Revisited''. Washington, DC: Math. Assoc. Amer., p. 59, 1967</ref> | ||