Circumscribed and Inscribed
Circumscribed and Inscribed
The terms circumscribed and inscribed refer, respectively, to polygons (straight-sided geometric figures) whose corners lie on an exterior circle or whose sides are all touched at one point each by an interior circle (i.e., whose sides are all tangent to a circle). For example, imagine that a circle is drawn around a triangle so that the circle touches all three vertices of the triangle. Then the circle is said to be circumscribed around the triangle, and the triangle is said to be inscribed within the circle.
A circle that circumscribes a polygon is said to be circumcircle around a polygon. A circle that inscribes a polygon is said to be a incircle into the polygon.
The concepts of circumscription and inscription can be extended to three (or more) dimensions. For example, a cone can be circumscribed around a pyramid if the vertices of the cone and pyramid coincide with each other, and the base of the cone circumscribes the base of the pyramid. In such a case, the pyramid is inscribed within the cone. As another example, a sphere can be inscribed within a cylinder if all parts of the cylinder are tangent to the sphere’s surface. Then the cylinder is circumscribed around the sphere.