# 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**.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**circumscribe** - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**circumscribed** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**circumscribed** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**circumscribe**