How to determine if a circle can be circumscribed about a quadrilateral

Question

I want to know about circumscribing circles about quadrilateral (how to do it, what that means etc.)

Answer 1

Construct the perpendicular bisectors of all four sides of the quadrilateral.  If they all cross at the same point, then that point is the circumcenter of the quadrilateral.  The radius of the circumcircle is the distance from the circumcenter to any of the four vertices of the quadrilateral.  To draw the circumcircle, place your compass point at the circumcenter and open the pencil end to any vertex, then draw the circle.  It will pass through all four vertices of the quadrilateral.

 

If the four perpendicular bisectors do not cross at the same point, there is no circumcenter and you cannot circumscribe a circle about the quadrilateral.