Definition:Inscribe

Definition

Let a geometric figure $A$ be constructed in the interior of another geometric figure $B$ such that:

$(1): \quad$ $A$ and $B$ have points in common

$(2): \quad$ No part of $A$ is outside $B$.

Then $A$ is inscribed inside $B$.

Circle in Polygon

A circle is inscribed in a polygon when it is tangent to each of the sides of that polygon:

Polygon in Circle

A polygon is inscribed in a circle when each of its vertices lies on the circumference of the circle:

That is, the vertices are concyclic.

Polygon in Polygon

A polygon is inscribed in another polygon when each of its vertices lies on the corresponding side of the other polygon.

Polyhedron in Sphere

A polyhedron is inscribed in a sphere when each of its vertices lies on the surface of the sphere.

Sphere in Polyhedron

A sphere is inscribed in a polyhedron when it is tangent to each of the faces of that polyhedron.

Also see

• Definition:Circumscribe

• Results about inscribe can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inscribed
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inscribed
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): inscribe