What Unique Properties Define a Cyclic Quadrilateral?

[Saad]

Here's an interesting question which is related to proofs, one of the hardest chapters of math:

If a circle can be drawn to pass through the 4 vertices of a Quadrilateral, we call this a "cyclic quadrilateral". What special properties do you think a cyclic quadrilateral has that wouldn't be true for any other quadrilateral?

 

[cookiemonster]

Just a quick guess: Right or acute angles?

cookiemonster

 

[arildno]

A cyclic quadrilateral satisfies Ptolemaios' theorem, which states, for vertices A,B,C,D:
AC*BD=AB*CD +BC*AD
(AC and BD diagonals)

I don't think non-cyclic quadrilaterals satisfy Pt. th.

 

[Chen]

Sum of every opposite pair of angles is π?

 

[ahrkron]

This smells like a question from a take-home test...