Question

Прямоугольный треугольник внутри этого Прямоугольный треугольника есть круг который со соприкасаются с 2 катетами и гипотенузой. и их размер ну (гипотенуза и т д, а не круга) 3,4,5 и надо найти радиус этого круга P.s ответ 1 см но как?

Answer 1

R=S/p, где S - площадь тр-ка, р - его полупериметр.
S=ab/2=3·4/2=6 см.
р=(3+4+5)/2=6 см.
r=6/6=1 см - это ответ.

Answer 2

Finding the radius of the circle inscribed in a right triangle

To find the radius of the circle inscribed in a right triangle, we can use the formula:

radius = (area of the triangle) / (semiperimeter of the triangle)

The semiperimeter of a triangle is half the sum of its three sides. In this case, the sides of the right triangle are given as 3, 4, and 5.

Let's calculate the area of the triangle first. We can use Heron's formula to find the area:

area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semiperimeter of the triangle, and a, b, and c are the lengths of its sides.

For the given right triangle with sides 3, 4, and 5, the semiperimeter is:

s = (3 + 4 + 5) / 2 = 6

Using Heron's formula, the area of the triangle is:

area = sqrt(6 * (6 - 3) * (6 - 4) * (6 - 5)) = sqrt(6 * 3 * 2 * 1) = sqrt(36) = 6

Now, we can calculate the radius of the inscribed circle:

radius = area / s = 6 / 6 = 1

Therefore, the radius of the circle inscribed in the given right triangle is 1 cm.

Please note that the answer provided is based on the given information and calculations. If there are any additional details or constraints, please let me know, and I'll be happy to assist you further.