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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 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.
Learn the definition, proof, and applications of Ptolemy's theorem, which relates the diagonals and sides of a cyclic quadrilateral. Explore examples, exercises, and the converse of Ptolemy's theorem.
Jun 2, 2024 · Learn what Ptolemy's Theorem is, how to prove it using similar triangles, and how to apply it to cyclic quadrilaterals, pentagons and rectangles. Discover the golden ratio and the Pythagorean theorem as corollaries of Ptolemy's Theorem.
Jul 1, 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.
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
Learn the formula and proof of Ptolemy’s theorem, which relates the areas and diagonals of a cyclic quadrilateral. Explore examples, worksheets, videos, and lesson plans for geometry students.
