A

polygon is called "

*inscribed*" in a

circle (more generally, a

polyhedron in a

sphere, or even a

polytope in a

`d`-1-

dimensional sphere) if all its

vertices occur on the sphere.

*Any* triangle is an inscribed triangle. For polygons with more sides, the condition becomes more interesting. For instance, a quadrilateral is inscribed in some sphere iff the sum of opposing angles is π (that' 180 degrees to any Babylonians who may have wandered in here today). [At least one implication follows immediately from properties of inscribed angles]

Contrast *circumscribed*.