โญ Circumscribed Circle Calculator
Calculate the circumscribed circle radius and area of a triangle.
What is a Circumscribed Circle?
A circle passing through all three vertices of a triangle. The circumcenter (O) is the intersection of the perpendicular bisectors of the three sides.
Circumscribed Circle Radius Formula
R = abc / (4S)
Here S is the triangle area, calculated using Heron's formula:
s = (a + b + c) / 2
S = โ(s(sโa)(sโb)(sโc))
Relationship with the Law of Sines
a / sin A = 2R
The diameter of the circumscribed circle equals each side divided by the sine of its opposite angle.
Position of the Circumcenter
Acute triangle: circumcenter is inside the triangle
Right triangle: circumcenter is at the midpoint of the hypotenuse (R = hypotenuse/2)
Obtuse triangle: circumcenter is outside the triangle