Ptolemy's Equality/Inequlity via Inversion
What is this about?
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.
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.
A proof is available on a separate page. Below are just two illustrations: