Search results
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]
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.
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.
Jun 2, 2024 · Ptolemy’s Theorem states, ‘For a quadrilateral inscribed in a circle, the sum of the products of each pair of opposite sides is equal to the product of its two diagonals’. Consider a quadrilateral ABCD with all of its vertices, i.e, A, B, C, D lying on a circle, thus, forming a cyclic quadrilateral.
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
Jul 13, 2024 · Ptolemy's Theorem. For a cyclic quadrilateral, the sum of the products of the two pairs of opposite sides equals the product of the diagonals. (1) (Kimberling 1998, p. 223). This fact can be used to derive the trigonometry addition formulas. Furthermore, the special case of the quadrilateral being a rectangle gives the Pythagorean theorem.
Ptolemy’s Theorem states that for a quadrilateral inscribed on a circle, the product of the lengths of the diagonals equals the sum of the products of the lengths of pairs of opposite sides.
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) [1]. With given side and diagonal lengths, Ptolemy's theorem of a cyclic quadrilateral states: p q = a c + b d. pq = ac+bd \\,. p q = a c + b d. (1)
Ptolemy's theorem for cyclic quadrilateral states that the product of the diagonals is equal to the sum of the products of opposite sides. From the figure below, Ptolemy's theorem can be written as $d_1 d_2 = ac + bd$
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.
