Geometric Primitives - 3D Math Primer for Graphics and Game Development - page 331

Figure 9.23
The incenter of a
triangle

The radius of the inscribed circle can be computed by dividing the area of
the triangle by its perimeter:

r In = A

p .

The inscribed circle solves the problem of finding a circle tangent to three
lines.
The circumcenter is the point in the triangle that is equidistant from
the vertices. It is the center of the circle that circumscribes the triangle.
The circumcenter is constructed as the intersection of the perpendicular
bisectors of the sides. Figure 9.24 shows the circumcenter of a triangle.

Figure 9.24
The circumcenter of
a triangle