circumradius

Find an expression for it in terms of the circumradius.

The length of one median is equal to the circumradius.

For regular polygons, the radius is the same as its circumradius.

Consequently these four possible triangles must all have circumcircles with the same circumradius.

However, the ratio of in-radius to circumradius does give a handle on triangle shape.

The circumradius R is given as a special case of Parameshvara's formula.

The semiperimeter is the sum of the inradius and twice the circumradius.

Its circumradius is times the length of its edge, a value it shares with the cube.

The circumradius often exceeds (and cannot be less than) the inner radius:

The center of the circle and its radius are called the circumcenter and the circumradius respectively.

The radii of these spheres are called the circumradius, the midradius, and the inradius.

Note that the ratio of the circumradius to the inradius is symmetric in p and q:

The circumradius R of a triangle can also be calculated from the semiperimeter and side lengths:

The circumcircle's radius is called the circumradius.

The following formulae for volume, surface area, and circumradius can be used if all faces are regular, with edge length a:

The following formulas involve the circumradius R and the inradius r:

A triangle is considered poor-quality if it has a circumradius to shortest edge ratio larger than some prescribed threshold.

See also Calculation of the circumradius (German)

Since an icosahedron has a circumradius divided by edge length less than one, the tetrahedral pyramids can be made with regular faces.

Inequality, complete system, planar convex set, area, perimeter, diameter, width, inradius, circumradius.

The circumscribed sphere has radius (the circumradius)

A shortcoming of this measure is that 3D slivers, which are bad cells, can have high values of short-edge to circumradius ratio.

The apothem a of a regular n-sided polygon with side length s, or circumradius R, can be found using the following formula:

The radius of the twelve-point sphere is one third of the circumradius of the reference tetrahedron.

Since a cuboctahedron has a circumradius divided by edge length equal to one, the triangles must be taller than equilateral to create a positive height.