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  "body": "\n## Statement\n\nIn 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:\n",
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