---
tag: KMB7KJJM6A
kind: statement
role: proposition
name: Ptolemy's inequality
aliases: [ptolemy-inequality]
sources:
  - wikipedia: en:7148302@r1342784682
    locator: Ptolemy's inequality
    note: adopted
    mention: wikipedia://en/7148302
    sections: [Statement]
same_as:
  wikidata: Q743775
  wikipedia: Ptolemy's inequality
inventory: [YHVDKJHZ59]
---

## Statement

In Euclidean geometry, **Ptolemy's inequality** relates the six [[distances|0C95TG69SG]] determined by four points in the [[plane|0XW7V9ZZ05]] or in a higher-dimensional space. It states that, for any four points $A$, $B$, $C$, and $D$, the following inequality holds: