How to determine if a group of points form an arс.

Question

I work on 3D printing project. The software that produces progam for 3D printer outputs a set of small straight lines when it needs to create a curve. However, new printer firmware understands true arc command and I want to write a code that would insert those commands where appropriate.
How can I determine that a set of 5 points form an arc (as in "a part of a circle") and find out the parameters of that circle? Could you point me in a right direction towards creating that algorythm? Thanks.

Answer 1

Hint: Use the inverse Ptolemy theorem: Test each quadruple in your pentuple.