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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.

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