Ptolemy's theorem gives a relationship between the side lengths and the diagonals of a cyclic quadrilateral; it is the equality case of Ptolemy's Inequality. Ptolemy's theorem frequently shows up as an intermediate step in problems involving inscribed figures.

Ptolemy's theorem states the relationship between the diagonals and the sides of a cyclic quadrilateral. It is a powerful tool to apply to problems about inscribed quadrilaterals. Let's prove this theorem.

Equilateral Triangle, Circumcircle, Point, Vertices, Distances, Ptolemy's theorem. Proposed Problem 63: Heptagon Regular, Side and Diagonals, Ptolemy's theorem.

In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle). The theorem is named after the Greek astronomer and mathematician Ptolemy (Claudius Ptolemaeus). [1]

Jan 15, 2019 · Ptolemy’s theorem, states that for a cyclic quadrilateral with side lengths a;b;c;d(in that order) and diagonals of lengths pand q, the product of the lengths of the diagonals equals the sum of the products of the lengths of the opposite sides, pq= ac+ bd. For a general convex quadrilateral, we have Ptolemy’s inequality: Theorem 1.

In this section, I will be presenting 2 problems to give a general idea of how Ptolemy's Theorem may be used. In speci c, I will try to explain motivational steps and include a write-up as I'd do it in a

Ptolemy’s theorem says that for a cyclic quadrilateral 𝐴𝐵𝐶𝐷, AC·BD = AB·CD + BC·AD. With ruler and a compass, draw an example of a cyclic quadrilateral. Label its vertices 𝐴, 𝐵, 𝐶, and 𝐷.

For , we use Ptolemy's theorem on cyclic quadrilateral to get . The sum of the lengths of the diagonals is so the answer is. Let denote the length of a diagonal opposite adjacent sides of length and , for sides and , and for sides and . Using Ptolemy's Theorem on the five possible quadrilaterals in the configuration, we obtain:

Problem 2: Ptolemy’s Theorem In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral (a quadrilateral whose vertices lie on a common circle).

Ptolemy’s theorem Suppose that four points A,B,C,Dlie on a circle in that order. Ptolemy’s Theorem concerns this configuration, and is perhaps the most important circle theorem which is not routinely taught in British schools: AB·CD+BC·DA= AC·BD, so in a cyclic quadrilateral, the sum of the products of opposite sides is the product of ...