A polygon is called "circumscribed" about a circle (more generally, a polyhedron about a sphere, or even a polytope about a d-1-dimensional sphere) if all its faces are tangent to the sphere.

Any triangle is a circumscribed triangle (about some circle). The centre of the circle must lie on all 3 angle bisectors, so the last statement is equivalent to saying that the 3 angle bisectors of any triangle meet at a single point. For polygons with more sides, the conditions become more interesting.

Contrast inscribed.

Log in or registerto write something here or to contact authors.