Question

Радіус кола, описаного навколо правильного многокутника, дорівнює 6 см, а радіус кола, вписаного у правильний многокутник, 3√3. Знайдіть кількість сторін многокутника

Answer 1

Ответ:

решение смотри на фотографии

Answer 2

Radius of the Circumscribed Circle

The radius of the circumscribed circle of a regular polygon is equal to 6 cm [[1]].

Radius of the Inscribed Circle

The radius of the inscribed circle of a regular polygon is equal to 3√3 cm [[2]].

To find the number of sides of the regular polygon, we can use the formula:

n = 360° / (180° - (360° / s))

where: - n is the number of sides of the polygon - s is the measure of each interior angle of the polygon in degrees

Finding the Measure of Each Interior Angle

The measure of each interior angle of a regular polygon can be found using the formula:

A = (n - 2) * 180° / n

where: - A is the measure of each interior angle of the polygon in degrees - n is the number of sides of the polygon

Solving for the Number of Sides

Let's substitute the given values into the formulas to find the number of sides of the regular polygon.

Using the formula for the measure of each interior angle:

A = (n - 2) * 180° / n

Substituting the value of the radius of the inscribed circle:

3√3 = (n - 2) * 180° / n

Simplifying the equation:

3√3n = 180n - 360

3√3n - 180n = -360

n(3√3 - 180) = -360

n = -360 / (3√3 - 180)

Using the formula for the number of sides:

n = 360° / (180° - (360° / s))

Substituting the value of the radius of the circumscribed circle:

6 = 360° / (180° - (360° / s))

Simplifying the equation:

6(180° - (360° / s)) = 360°

1080° - 2160° / s = 360°

1080° - 2160° = 360°s

-1080° = 360°s

s = -1080° / 360°

s = -3

Since the number of sides cannot be negative, we can conclude that there is an error in the given information or calculations. Please double-check the values provided.