查看“︁婆羅摩笈多定理”︁的源代码

[[File:Brahmaguptra's theorem.svg|thumb|婆羅摩笈多定理指出AF=FD]]

'''婆罗摩笈多定理'''指出：若圆内接[[四边形]]的[[对角线]]相互[[垂直]]，则垂直于一边且过对角线交点的直线將平分对边。[[婆罗摩笈多]]是[[印度]]数学家。

==证明==
:因为<math>\angle AMF = \angle EMC = \angle MBC = \angle MAD</math>

:所以<math> AF = MF</math>

:<math>\angle FMD = 90^\circ - \angle AMF = 90^\circ -\angle MAD = \angle FDM </math>

:因此 <math>MF = DF</math>

:<math>AF = MF = DF</math>

:即<math>EF</math>平分<math>AD</math>

==婆羅摩笈多四邊形==
婆羅摩笈多四邊形是四邊形，其邊長順序分別為<math>a_1 b_3, a_3 b_2, a_2 b_3, a_3 b_1</math>，且<math>a_1^2 + a_2^2 = a_3^2</math>、<math>b_1^2 + b_2^2 = b_3^2</math>。

婆羅摩笈多四邊形既是[[圓內接四邊形]]，又是[[正交四边形]]（對角線垂直的四边形）。

==参考文献==
*{{cite book|author=Harold Scott MacDonald Coxeter; Greitzer, S. L|title=''Geometry Revisited''|location=Washington, DC|publisher=Math. Assoc. Amer|year=1967|pages=59}}
==外部链接==
*{{MathWorld|urlname=BrahmaguptasTheorem|title=Brahmagupta's theorem}}
* [http://www.cut-the-knot.org/Curriculum/Geometry/Brahmagupta.shtml Brahmagupta's Theorem] {{Wayback|url=http://www.cut-the-knot.org/Curriculum/Geometry/Brahmagupta.shtml |date=20200922014039 }} at [[cut-the-knot]]

[[Category:四邊形]]
[[Category:平面幾何]]
[[Category:几何定理|Brahmagupta]]