Theorem of Ptolemy

Ptolemy's Theorem states that in a cyclic quadrilateral— a four-sided figure with all vertices on the same circle — the product of the lengths of the two diagonals equals the sum of the products of the pairs of opposite sides. In formula form: \( AC \times BD = AB \times CD + BC \times DA \). This relationship helps us understand how side lengths and diagonals interact in circular polygons, and is useful in geometry, trigonometry, and even astronomy for calculations involving circular shapes.