If the circumradius of a triangle is 40 cm, then radius of the circle is:

Concept:

Nine-point circle:

Circle exists is a non-trivial theorem of Euclidean geometry. The nine-point circle is tangent to the incircle, has a radius equal to half the circumradius, and its center is the midpoint of the segment connecting the orthocenter and the circumcenter, upon which the centroid also falls.

Then,

The required radius of the nine-point circle is 40/2 = 20 cm.

Additional Information

Circumradius:

The circumradius of a cyclic polygon is the radius of the circumscribed circle of that polygon. For a triangle, it is the measure of the radius of the circle that circumscribes the triangle. Since every triangle is cyclic, every triangle has a circumscribed circle or a circumcircle.