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МатематикаВопрос:
r - ? A right-angled triangle ABC has legs AC = 6 and BC = 8. A circle is inscribed in the triangle. What is the radius of the inscribed circle?
Ответ:
Краткое пояснение: Радиус вписанной окружности в прямоугольный треугольник можно найти по формуле r = (a + b - c) / 2, где a и b - катеты, а c - гипотенуза.
Пошаговое решение:
- Найдем длину гипотенузы AB по теореме Пифагора: AB2 = AC2 + BC2.
- AB2 = 62 + 82 = 36 + 64 = 100.
- AB = √100 = 10.
- Используем формулу для радиуса вписанной окружности в прямоугольный треугольник: r = (AC + BC - AB) / 2.
- r = (6 + 8 - 10) / 2.
- r = (14 - 10) / 2.
- r = 4 / 2 = 2.
Ответ: 2
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