For triangles whose sides are Pythagorean triples, the radius of this circle is a whole number.
The radius of this circle is equal to the area divided by the semiperimeter of its generating triangle. For triangles whose sides are Pythagorean triples, the radius of this circle is a whole number. Its center can be found by taking the weighted average of vertices of the generating triangle using opposite side lengths as weights, and it splits the triangle sides into lengths equal to the factors in Heron's Formula. The center of this circle is at the concurrence of its generating triangle's angle bisectors, and is the same distance from the three sides of that triangle. Name this circle that is tangent to all three sides of a triangle.
The radius of this circle is equal to the area divided by the semiperimeter of its generating triangle.
incircle [or inscribed circle]