In any given triangle, we can always find a circle that goes through each of its vertices, and a circle inside the triangle that is tangent to all three sides. The first is called circumcircle and its radius is the circumradius. The second is called incircle and its radius is the inradius. The center of the circumcircle (the circumcenter) can be found in the intersection of the three perpendicular bisectors of the triangle. The center of the incircle (the incenter) can be found in the intersection of the three angle bisectors of the triangle.

Note that at the beginning of the chapter we have four different formulas to find the area of a triangle. One of them uses the circumradius, and other uses the inradius.