Inscribed Circle (Inradius)
Side a
Side b
Side c
The inscribed circle (incircle) is the largest circle that fits inside a triangle, tangent to all three sides. Its radius (inradius) equals the triangle area divided by the semi-perimeter.
- 1r = Area / s
- 2Where s = (a+b+c)/2 (semi-perimeter)
- 3Area found via Heron's formula
- 4Centre is at the intersection of the angle bisectors (incentre)
Triangle 3, 4, 5=r = 6/6 = 1
Triangle 5, 12, 13=r = 30/15 = 2
| Sides | Area | Semi-perimeter | Inradius r |
|---|---|---|---|
| 3,4,5 | 6 | 6 | 1 |
| 5,12,13 | 30 | 15 | 2 |
| 8,15,17 | 60 | 20 | 3 |
| 6,8,10 | 24 | 12 | 2 |
References
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