# Ptolemy's theorem. How to prove?

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 $B,D$.

-

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