Circumscribed Circle (Circumradius)
Side a
Side b
Side c
The circumscribed circle (circumcircle) of a triangle is the unique circle passing through all three vertices. The circumradius R is the radius of this circle.
- 1R = (a × b × c) / (4 × Area)
- 2Where Area = √(s(s−a)(s−b)(s−c)) by Heron's formula
- 3s = (a + b + c) / 2 (semi-perimeter)
- 4For a right triangle: R = hypotenuse / 2
Triangle with sides 3, 4, 5=R = (3×4×5)/(4×6) = 2.5
Equilateral triangle, side = 6=R = 6/√3 = 3.464
| Sides | Area | Circumradius R |
|---|---|---|
| 3,4,5 | 6 | 2.50 |
| 5,5,6 | 12 | 3.13 |
| 6,6,6 | 15.59 | 3.46 |
| 5,12,13 | 30 | 6.50 |
References
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