Question

Прямоугольный треугольник abc с катетами 18см и 24см вписан в окружность найдите радиус этой окружности в сантиметрах

Answer 1

Дано:треугольник ABC- вписанный
AB=18 см
AC=24 см 
R=?
Решение:
BC^2=AC^2+AB^2=576+324=900(30)
R=30/2=15
Ответ:15 см

Answer 2

Finding the Radius of the Inscribed Circle

To find the radius of the circle inscribed in the right triangle ABC with legs measuring 18 cm and 24 cm, we can use the properties of a right triangle and the relationship between the radius of the inscribed circle and the triangle's sides.

Let's break down the solution step by step:

1. In a right triangle, the radius of the inscribed circle is equal to half the length of the hypotenuse. This can be derived from the fact that the incenter (the center of the inscribed circle) is equidistant from all three sides of the triangle.

2. The hypotenuse of the right triangle ABC can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse can be calculated as follows:

- Using the given lengths of the legs: - Leg AB = 18 cm - Leg BC = 24 cm

- Applying the Pythagorean theorem: - Hypotenuse AC = √(AB^2 + BC^2)

3. Once we have the length of the hypotenuse, we can find the radius of the inscribed circle by dividing it by 2.

Let's calculate the radius using the given measurements:

1. Calculate the hypotenuse AC using the Pythagorean theorem: - AB^2 + BC^2 = 18^2 + 24^2 = 324 + 576 = 900 - AC = √900 = 30 cm 2. Divide the length of the hypotenuse by 2 to find the radius of the inscribed circle: - Radius = AC/2 = 30/2 = 15 cm

Therefore, the radius of the inscribed circle in the right triangle ABC, with legs measuring 18 cm and 24 cm, is 15 centimeters.