Question

Периметр правильного четырёхугольника, описанного около окружности, на 6 см больше периметра правильного шестиугольника, вписанного в эту окружность Найдите радиус окружности

Answer 1

у меня так получилось, думаю что это правильно

Answer 2

Perimeter of a Regular Quadrilateral Inscribed in a Circle

To find the radius of the circle, we need to compare the perimeters of a regular quadrilateral (four-sided polygon) circumscribed around the circle and a regular hexagon (six-sided polygon) inscribed in the same circle.

Let's assume that the side length of the regular quadrilateral is x and the side length of the regular hexagon is y.

The perimeter of the regular quadrilateral is given by 4 times the side length, so it is equal to 4x.

The perimeter of the regular hexagon is given by 6 times the side length, so it is equal to 6y.

According to the given information, the perimeter of the quadrilateral is 6 cm more than the perimeter of the hexagon. Mathematically, we can express this as:

4x = 6y + 6

To find the radius of the circle, we need to relate the side length of the hexagon to the radius. For a regular hexagon, the side length is equal to the radius multiplied by the square root of 3.

y = r * √3

Substituting this into the previous equation, we get:

4x = 6(r * √3) + 6

Simplifying the equation, we have:

4x = 6r√3 + 6

Now, we can solve for the radius of the circle.

Please note that I was unable to find a specific numerical solution for this equation in the search results. However, you can use the equation provided to solve for the radius by substituting the known values for x and solving for r.