What is the formula?
Might you be seeking the radius of a triangles inscribed or circumscbibed circles?
*--Incenter
The incenter is the point where the three angle bisectors intersect and is the center of the incircle.
*--Circumcenter
The circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle and the center of the circumscribed circle about the triangle.
*--Excenters
The points of intersection of an internal bisector of an interior angle at one vertex and the bisectors of the exterior angles of the other two vertices.
*--Incircle
The internal circle tangent to the three sides and the incenter as center.
The radius of the inscribed circle is r = A/s where A = the area of the triangle and s = the semi-perimeter = (a + b + c)/2, a, b, and c being the three sides.
The radius of the inscribed circle may also be derived from r = ab/(a + b + c).
The radius of the inscribed circle may also be derived from the particular m and n used in deriving a Pythagoraen Triple triangle by r = n(m - n).
If x, y, and z are the points of contact of the incircle with the sides of the triangle A, B, C, then Cx = Cy = s - c, Bx = Bz = s - b, and Ay = Az = s - a.
*--Circumcircle
The external circle touching the three vertices of a triangle with center at the circumcenter.
The radius of the circumcircle is R = abc/4A, a, b, and c being the three sides and A being the area of the triangle.
Second Law of Sines - With R = the circumcircle radius, a/sinA = b/sinB = c/sinC = 2R.
*--Excircles
The excircles, centered at the excenters, lie outside of the triangle and touch the three sides, one side of the triangle externally and two sides extended outside the triangle.
*--Incircle-Excircle Relationship
For an incircle radius of r and excircle radii of ra, rb, and rc, 1/r = 1/ra + 1/rb + 1/rc.
*--Excircle-Circumcircle Relationship
For a circumcircle radius of R, ra + rb + rc - r = 4R.
*--The incircle radius r, the circumcircle radius R, and the distance between the two centers s, are related to one another by R^2 = s^2 + 2Rr.