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:
Figure for derivation of radius of circumcircleIf 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