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  2. Cyclic quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Cyclic_quadrilateral

    If a cyclic quadrilateral has side lengths that form an arithmetic progression the quadrilateral is also ex-bicentric. If the opposite sides of a cyclic quadrilateral are extended to meet at E and F, then the internal angle bisectors of the angles at E and F are perpendicular. [13]

  3. Ptolemy's theorem - Wikipedia

    en.wikipedia.org/wiki/Ptolemy's_theorem

    Ptolemy's theorem is a relation among these lengths in a cyclic quadrilateral. = + 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).

  4. Quadrilateral - Wikipedia

    en.wikipedia.org/wiki/Quadrilateral

    A convex quadrilateral is cyclic if and only if opposite angles sum to 180°. Right kite: a kite with two opposite right angles. It is a type of cyclic quadrilateral. Harmonic quadrilateral: a cyclic quadrilateral such that the products of the lengths of the opposing sides are equal. Bicentric quadrilateral: it is both tangential and cyclic.

  5. 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.

  6. Brahmagupta theorem - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta_theorem

    In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. [1] It is named after the Indian mathematician Brahmagupta (598-668). [2]

  7. List of mathematical shapes - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_shapes

    Polygons named for their number of sides Monogon — 1 sided; Digon — 2 sided; Triangle. Acute triangle; ... Quadrilateral. Cyclic quadrilateral. square; kite ...

  8. Concyclic points - Wikipedia

    en.wikipedia.org/wiki/Concyclic_points

    A cyclic polygon with an even number of sides has all angles equal if and only if the alternate sides are equal (that is, sides 1, 3, 5, … are equal, and sides 2, 4, 6, … are equal). [ 11 ] A cyclic pentagon with rational sides and area is known as a Robbins pentagon .

  9. Right kite - Wikipedia

    en.wikipedia.org/wiki/Right_kite

    In Euclidean geometry, a right kite is a kite (a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other) that can be inscribed in a circle. [1] That is, it is a kite with a circumcircle (i.e., a cyclic kite). Thus the right kite is a convex quadrilateral and has two opposite right ...