Question

Довжина кола, описаного навколо правильного чотирикутника, дорівнює 24π см. Знайдіть периметр чотирикутника

Answer 1

Радиус описанной окружности квадрата равен: 

R =[(корень из 2) / 2] * а,
где а - сторона квадрата.
Периметр - это четыре стороны: Р = 4а,
Длина окружности L = 2*Пи *R.

Answer 2

Calculating the Perimeter of a Quadrilateral Inscribed in a Circle

To find the perimeter of the quadrilateral inscribed in a circle, we can use the given information about the circle's circumference and the properties of a quadrilateral inscribed in a circle.

Given: - Circumference of the circle, C = 24π cm

We need to find the perimeter of the quadrilateral.

Solution

The perimeter of the quadrilateral can be found using the following steps:

1. Understanding the Relationship Between the Circle and the Quadrilateral - A quadrilateral inscribed in a circle is a cyclic quadrilateral, and the opposite angles of a cyclic quadrilateral are supplementary.

2. Using the Circumference of the Circle to Find the Radius - The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. - From the given circumference, we can find the radius of the circle: C = 2πr - 24π = 2πr - Solving for r: r = 12 cm

3. Calculating the Perimeter of the Quadrilateral - The perimeter of the quadrilateral can be found using the lengths of its sides and the properties of a cyclic quadrilateral.

4. Using the Radius to Find the Side Lengths of the Quadrilateral - The sides of the quadrilateral are tangents to the circle, and the lengths of the tangents from an external point to a circle are equal. - Since the quadrilateral is inscribed in the circle, the lengths of the sides are equal to the radius of the circle: AB = BC = CD = DA = 12 cm

5. Calculating the Perimeter - The perimeter of the quadrilateral is the sum of its side lengths: Perimeter = AB + BC + CD + DA - Substituting the values: Perimeter = 12 + 12 + 12 + 12 = 48 cm

Answer

The perimeter of the quadrilateral inscribed in the circle is 48 cm.