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  2. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). [ 1 ]

  3. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    Ptolemy's theorem expresses the product of the lengths of the two diagonals e and f of a cyclic quadrilateral as equal to the sum of the products of opposite sides: [9]: p.25 [2] e f = a c + b d , {\displaystyle \displaystyle ef=ac+bd,}

  4. Brahmagupta's formula - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta's_formula

    This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.

  5. Concyclic points - Wikipedia

    en.wikipedia.org/wiki/Concyclic_points

    By Ptolemy's theorem, if a quadrilateral is given by the pairwise distances between its four vertices A, B, C, and D in order, then it is cyclic if and only if the product of the diagonals equals the sum of the products of opposite sides:

  6. Category:Theorems about quadrilaterals and circles - Wikipedia

    en.wikipedia.org/wiki/Category:Theorems_about...

    Brahmagupta theorem; Brahmagupta's formula; J. Japanese theorem for cyclic quadrilaterals; N. ... Pitot theorem; Ptolemy's theorem

  7. 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]

  8. AOL Mail for Verizon Customers - AOL Help

    help.aol.com/products/aol-mail-verizon

    AOL Mail welcomes Verizon customers to our safe and delightful email experience!

  9. Ptolemy's inequality - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_inequality

    Polarization identity – Formula relating the norm and the inner product in a inner product space; Ptolemy – Roman astronomer and geographer (c. 100–170) Ptolemy's table of chords – 2nd century AD trigonometric table; Ptolemy's theorem – Relates the 4 sides and 2 diagonals of a quadrilateral with vertices on a common circle