# Definition:Circumscribe

## Definition

A geometric figure $A$ circumscribes another geometric figure $B$ when the vertices of $B$ lie on the boundary of $A$.

### Circle around Polygon

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

### Polygon around Circle

A polygon is circumscribed around a circle when each of its sides is tangent to the circumference of the circle:

### Polygon around Polygon

A polygon is circumscribed around another polygon when each of its sides passes through each of the vertices of the other polygon.

### Sphere around Polyhedron

A sphere is circumscribed around a polyhedron when its surface passes through each of the vertices of that polyhedron:

### Polyhedron around Sphere

A polyhedron is circumscribed around a sphere when each of its faces is tangent to the surface of the sphere:

## Also defined as

Some sources are not particularly careful to specify that the vertices of the circumscribed figure must all lie on the boundary of the circumscribing figure, but merely that one encloses the other.

## Also known as

As well as circumscribed around, the following can also be seen:

The more archaic circumscribed without can also occasionally be encountered.

## Examples

### Prism in Cylinder

A prism $\PP$ is circumscribed by a cylinder $\CC$ if and only if all the edges of $\PP$ lie on the surface of $\CC$.

## Also see

• Results about circumscribe can be found here.