The diameter of each small star's circumscribed circle is 2 units.

This ratio is equal to the diameter of the circumscribed circle of the given triangle.

Cyclic quadrilateral: the four vertices lie on a circumscribed circle.

All triangles are cyclic, i.e. every triangle has a circumscribed circle.

The circumscribed sphere is the three-dimensional analogue of the circumscribed circle.

This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic.

A cyclic polygon, which is inscribed in a circle (the circumscribed circle)

The circle containing the vertices of a triangle is called the circumscribed circle of the triangle.

With the sides of the cyclic quadrilateral being a, b, c, and d, the radius R of the circumscribed circle is:

If circles are circumscribed about and inscribed in a square, the circumscribed circle is double of the inscribed square.

All vertices of a regular polygon lie on a common circle (the circumscribed circle), i.e., they are concyclic points.

If the object does not have an obvious center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere.

The angles which the circumscribed circle forms with the sides of the triangle coincide with angles at which sides meet each other.

The remaining two solutions (shown in red in Figure 12) correspond to the inscribed and circumscribed circles, and are called Soddy's circles.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

Minimum circumscribed circle (MCC): It is defined as the smallest circle which encloses whole of the roundness profile.

The dual polygon of a tangential polygon is a cyclic polygon, which has a circumscribed circle passing through each of its vertices.

Since such a homothety is a congruence, this gives property 5, and also the Johnson circles theorem since congruent triangles have circumscribed circles of equal radius.

The resulting polar graph is then circumscribed with the smallest circle possible and the difference between this circumscribed circle and the nominal ball diameter is the variation.

If an orthodiagonal quadrilateral is also cyclic, the distance from the circumcenter (the center of the circumscribed circle) to any side equals half the length of the opposite side.

As with dual polyhedra, one can take a circle (be it the inscribed circle, circumscribed circle, or if both exist, their midcircle) and perform polar reciprocation in it.

Some examples are given by inscribed and circumscribed circles of polygons, lines intersecting and tangent to conic sections, the Pappus and Menelaus configurations of points and lines.

Every circle has an inscribed triangle with any three given angle measures (summing of course to 180 ), and every triangle can be inscribed in some circle (which is called its circumscribed circle).

Not every polygon has a circumscribed circle, as the vertices of a polygon do not need to all lie on a circle, but every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

Even if a polygon has a circumscribed circle, it may not coincide with its minimum bounding circle; for example, for an obtuse triangle, the minimum bounding circle has the longest side as diameter and does not pass through the opposite vertex.