Definition:Circumscribe

Circle
A circle is circumscribed around a polygon when it passes through each of the vertices of that polygon:


 * Circumscribe.png

Not all polygons can be circumscribed.

Here is an example of one that can not:


 * Circumscribe-not.png

All triangles can be uniquely circumscribed.

Euclid's Terminology
Euclid, in his definitions for Book IV: Definition 3 of, refers to this as "a rectilineal figure inscribed in a circle".