Question

ПОМОГИТЕ ПОЖАЛУЙСТА, ОЧЕНЬ НУЖНА ВАША ПОМОЩЬ! ❤️ 7. Радіус кола, описаного навколо правильного трикутника, дорівнює 10 см. Знайдіть радіус вписаного кола​

Answer 1

Ответ:
r=5см.

Решение:
R:r=2:1
r=R:2=10:2=5см

Answer 2

Finding the Radius of the Inscribed Circle in a Triangle

To find the radius of the inscribed circle (also known as the incircle) in a triangle, we can use the formula:

Radius of inscribed circle = Area of the triangle / Semiperimeter of the triangle

The semiperimeter of the triangle is half of the perimeter, which can be calculated as:

Semiperimeter = (a + b + c) / 2

Where 'a', 'b', and 'c' are the lengths of the sides of the triangle.

In this case, we are given that the radius of the circumscribed circle (circumcircle) of the equilateral triangle is 10 cm. To find the radius of the inscribed circle, we need to calculate the semiperimeter and the area of the triangle.

Calculating the Semiperimeter

The equilateral triangle has three equal sides, so the semiperimeter can be calculated as: Semiperimeter = (10 + 10 + 10) / 2 = 15 cm

Calculating the Area of the Triangle

The area of an equilateral triangle can be calculated using the formula: Area = (sqrt(3) / 4) * side^2

Substituting the given side length (10 cm) into the formula: Area = (sqrt(3) / 4) * 10^2 = (sqrt(3) / 4) * 100 = 25sqrt(3) cm^2

Finding the Radius of the Inscribed Circle

Now, we can use the formula for the radius of the inscribed circle: Radius of inscribed circle = Area of the triangle / Semiperimeter of the triangle

Substituting the calculated values: Radius of inscribed circle = (25sqrt(3)) / 15 = (5sqrt(3)) / 3 ≈ 2.89 cm

Therefore, the radius of the inscribed circle in the equilateral triangle is approximately 2.89 cm.