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.