Question

Радиус окружности, описанной около правильного треугольника, равен 12 см. Найдите радиус окружности, вписанной в треугольник Очень срочно,помогите пожалуйста!!!!

Answer 1

Пользуемся формулой; r=R*cos180/n,где r-радиус вписанной окр.,R-описанной,n-число сторон!
180/3(т.к у нас треугольник)=60
cos60=1/2
r=R*1/2=12*1.2=6
Ответ:6

Answer 2

R описаной окружности около правильного треугольника равен а√3/3 где а - сторона
подставляем 12=а√3/3 отсюда а=12√3
r вписаной окружности в правильный треугольник равен а√3/6
отсюда r=6

Answer 3

Radius of the Circumscribed Circle

The radius of the circumscribed circle of a regular triangle can be found using the formula:

Radius of the circumscribed circle = (side length of the triangle) / (2 * sin(60 degrees))

Since the triangle is regular, all sides are equal in length. Let's denote the side length of the triangle as 's'.

Therefore, the radius of the circumscribed circle is:

Radius of the circumscribed circle = s / (2 * sin(60 degrees))

Now, let's substitute the given information into the formula.

Given: Radius of the circumscribed circle = 12 cm

We need to find the side length of the triangle, which will help us find the radius of the inscribed circle.

To find the side length of the triangle, we can rearrange the formula as follows:

s = (Radius of the circumscribed circle) * (2 * sin(60 degrees))

Substituting the given value:

s = 12 cm * (2 * sin(60 degrees))

To calculate the value of sin(60 degrees), we can use a trigonometric table or calculator. The value of sin(60 degrees) is approximately 0.866.

s = 12 cm * (2 * 0.866) = 20.784 cm

Therefore, the side length of the triangle is approximately 20.784 cm.

Radius of the Inscribed Circle

The radius of the inscribed circle of a regular triangle can be found using the formula:

Radius of the inscribed circle = (side length of the triangle) / (2 * tan(60 degrees))

Using the side length of the triangle we found earlier (s ≈ 20.784 cm), we can calculate the radius of the inscribed circle.

Radius of the inscribed circle = 20.784 cm / (2 * tan(60 degrees))

To calculate the value of tan(60 degrees), we can use a trigonometric table or calculator. The value of tan(60 degrees) is approximately 1.732.

Radius of the inscribed circle = 20.784 cm / (2 * 1.732) ≈ 6 cm

Therefore, the radius of the inscribed circle is approximately 6 cm.

I hope this helps! Let me know if you have any further questions.