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  2. Bretschneider's formula - Wikipedia

    en.wikipedia.org/wiki/Bretschneider's_formula

    Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]

  3. Brahmagupta's formula - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta's_formula

    In Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any convex cyclic quadrilateral (one that can be inscribed in a circle) given the lengths of the sides. Its generalized version, Bretschneider's formula, can be used with non-cyclic quadrilateral.

  4. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle. Usually the quadrilateral is assumed to be convex, but there are also crossed cyclic quadrilaterals. The formulas and properties given below are valid in the convex case.

  5. Varignon's theorem - Wikipedia

    en.wikipedia.org/wiki/Varignon's_theorem

    An arbitrary quadrilateral and its diagonals. Bases of similar triangles are parallel to the blue diagonal. Ditto for the red diagonal. The base pairs form a parallelogram with half the area of the quadrilateral, A q, as the sum of the areas of the four large triangles, A l is 2 A q (each of the two pairs reconstructs the quadrilateral) while that of the small triangles, A s is a quarter of A ...

  6. Ex-Google CEO Eric Schmidt says human operators need to have ...

    www.aol.com/ex-google-ceo-eric-schmidt-163658792...

    Former Google CEO Eric Schmidt says human-directed AI-controlled drones are the future of war. Schmidt's startup, White Stork, is developing drones for Ukraine to use in its war with Russia.

  7. Heron's formula - Wikipedia

    en.wikipedia.org/wiki/Heron's_formula

    Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the quadrilateral to zero. Brahmagupta's formula gives the area ⁠ K {\displaystyle K} ⁠ of a cyclic quadrilateral whose sides have lengths ⁠ a , {\displaystyle a,} ⁠ ⁠ b , {\displaystyle b,} ⁠ ⁠ c , {\displaystyle c ...

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