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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.
Формула
r = A/s where A = area, s = semi-perimeter
- r
- inradius (inscribed circle radius) (length)
- A
- triangle area (length²)
- s
- semi-perimeter (length)
Водич корак по корак
- 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)
Worked Examples
Инпут
Triangle 3, 4, 5
Резултат
r = 6/6 = 1
Инпут
Triangle 5, 12, 13
Резултат
r = 30/15 = 2
Frequently Asked Questions
What is the incentre of a triangle?
The incentre is the center of the inscribed circle, located at the intersection of the three angle bisectors.
Is the inradius always smaller than the circumradius?
Yes, for any triangle, the inradius r is always less than the circumradius R.
How many inscribed circles can a triangle have?
Exactly one. The inscribed circle is unique and is the largest circle that fits inside the triangle.
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