Derivation of Formula for Radius of Circumcircle
The formula for the radius of the circle circumscribed about a triangle (circumcircle) is given by
R=abc4At
where At is the area of the inscribed triangle.
Derivation:
If you have some questions about the angle θ shown in the figure above, see the relationship between inscribed and central angles.
From triangle BDO
sinθ=a/2R
sinθ=a2R
At = area of triangle ABC
At=12bcsinθ
At=12bc(a2R)
At=abc4R
R=abc4At