Cyclic quadrilateral

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In geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. The vertices are said to be concyclic.

• Opposite angles are supplementary angles (adding up to 180 degrees, π radians or 200 grads).
• The area of a cyclic quadrilateral is given by Brahmagupta's formula as long as the sides are given.
• The area of a cyclic quadrilateral is maximal among all quadrilaterals having the same side lengths.
• Exterior angles are equal to the opposite interior angles.
• When the diagonals are drawn, two pairs of similar triangles are formed.
• The product of the two diagonals is equal to the sum of the products of opposite sides (Ptolemy's Theorem).

See also

• Cyclic polygon

External links

• Book 3, Proposition 22 of Euclid's Elements
• Cyclic quadrilateral theorem by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas".
• Incenters in Cyclic Quadrilateral at cut-the-knot
• Four Concurrent Lines in a Cyclic Quadrilateral at cut-the-knotde:Sehnenviereck