A quadrilateral in which all four vertices are concyclic (lie on the same circle). The following properties are found in every cyclic quadrilateral:

  • Opposite angles are Supplementary Angles (adding up to either 180 in degrees or pi in radians, depending on what you’re using).
  • Exterior angles are equal to the opposite interior angles.
  • When the diagonals are drawn, two pairs of similar triangles are formed.
  • The area can be determined by Brahmagupta's formula as well as Hero's formula as long as all sides are known.
  • Of all quadrilaterals with given four sides, the cyclic one is of greatest area.
  • The product of the two diagonals is equal to the sum of the products of opposite sides.
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