Як розрахувати Inscribed Circle
Що таке Inscribed Circle?
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)
Покрокова інструкція
- 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)
Розв'язані приклади
Введення
Triangle 3, 4, 5
Результат
r = 6/6 = 1
Введення
Triangle 5, 12, 13
Результат
r = 30/15 = 2
Часті запитання
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.
Готові порахувати? Спробуйте безкоштовний калькулятор Inscribed Circle
Спробуйте самі →