KnowraPtolemy's inequalityLinked fromLinked fromThe 6 pages that link to Ptolemy's inequality, each with the reason it gives.All 6Broader topic 1Related 1Compared with 4Ptolemy's theoremCompared with: Equality holds exactly for cyclic quadrilaterals, extending the theorem beyond its stated case.Geometric inequalityBroader topic: It distinguishes cyclic quadrilaterals through a bound that becomes equality for them.Euler's quadrilateral theoremCompared with: It bounds a product rather than equating sums of squared lengths.Hadwiger–Finsler inequalityCompared with: It is a classical metric inequality for polygons, but concerns quadrilateral diagonals rather than triangle area.Casey's theoremCompared with: It extends the equality principle underlying Casey's theorem beyond cyclic configurations.Erdős–Mordell inequalityRelated: A related metric inequality can help bound sums of distances in geometric proofs.