# Ptolemy's Equality/Inequlity via Inversion

### What is this about?

### Ptolemy's Theorem

For four distinct coplanar points $A,$ $B,$ $C,$ and $D,$

$AB\cdot CD+AD\cdot BC\ge AC\cdot BD.$

The equality only reached when the four points are concyclic.

### Hint

There are several known proofs of this well known and useful result; the applet above was intended to suggest that inversion might help furnish another proof.

### Proof

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