A cyclic pentagon is a not necessarily regular pentagon on whose polygon vertices a circle may be circumscribed. Let such a pentagon have edge lengths a_1, ..., a_5, and area K, and let σ_i congruent Π_i(a_1^2, a_2^2, a_3^2, a_4^2, a_5^2) denote the ith-order symmetric polynomial on the five variables consisting of the squares a_i^2 of the pentagon side lengths a_i, so

concyclic | cyclic hexagon | cyclic polygon | cyclic quadrilateral