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For distinct points $A, B, C, D$ on a plane, we have $(AB).(CD) + (AD).(BC) \geq (AC).(BD)$. Equality happens if and only if $A,B,C,D$ are collinear or concyclic with $A,C$ separating $B,D$.

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Please check here http://planetmath.org/encyclopedia/ProofOfPtolemysInequality.html

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Searching on $\text{Google}$ gives me the following link, where the solution is presented.

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