KnowraPtolemy's theoremLinked fromLinked fromThe 16 pages that link to Ptolemy's theorem, each with the reason it gives.All 16Related 9Compared with 7Law of cosinesCompared with: It is a distinct metric theorem sometimes used to derive triangle side relations.Ptolemy's inequalityCompared with: This is the equality case of the inequality, characterizing when its bound is sharp.Euler's quadrilateral theoremCompared with: It gives a different diagonal-side relation, but only for cyclic quadrilaterals.Pedoe's inequalityCompared with: It is another sharp geometric relation, but concerns cyclic quadrilaterals rather than paired triangles.Clifford's circle theoremsCompared with: It concerns metric lengths on a circle, rather than incidence across successive circles.Five circles theoremCompared with: It concerns the same circle geometry but gives a metric identity instead of a new concyclicity result.Pompeiu's theoremCompared with: Both relate distances in cyclic configurations, but Ptolemy's theorem requires a quadrilateral.