Ptolemy's Theorem

Ptolemy's Theorem states that in a cyclic quadrilateral— a four-sided figure with all vertices on a circle—the sum of the products of its two pairs of opposite sides equals the product of its two diagonals. Mathematically, if the quadrilateral has sides a, b, c, d, with diagonals p and q, then: a·c + b·d = p·q. This relationship helps in relating side lengths and diagonals in such figures, and has applications in astronomy, navigation, and geometry for solving problems involving distances and angles in circular arrangements.