الدائرة : الدائرة ومحيطها - حل مسائل

The video tutorial explains how to find the exact circumference of a circle that surrounds a right triangle with legs measuring 7 meters and 3 meters. It uses the Pythagorean theorem to determine the diameter of the circle, which is the hypotenuse of the triangle. The circumference is then calculated using the formula C = πD. Additionally, the video explores a scenario where a circle is inscribed in a square with a side length of 10 feet, showing that the circle's diameter equals the side of the square, and thus the circumference is π times the side length.

What is the relationship between the hypotenuse of the triangle and the circle in the given problem?

• The hypotenuse is the diameter of the circle.

• The hypotenuse is the circumference of the circle.

• The hypotenuse is the radius of the circle.

• The hypotenuse is unrelated to the circle.

How do you calculate the diameter of the circle using the Pythagorean theorem?

• Divide the sum of the triangle's legs by two.

• Subtract the squares of the triangle's legs and take the square root.

• Multiply the triangle's legs and take the square root.

• Add the squares of the triangle's legs and take the square root.

What is the formula used to calculate the perimeter of the circle?

• Perimeter = π × radius

• Perimeter = π × diameter

• Perimeter = 2π × diameter

• Perimeter = 2π × radius

In the scenario where the circle is inscribed in a square, what is the diameter of the circle?

• Twice the square's side length

• Half of the square's side length

• Equal to the square's side length

• Equal to the square's diagonal

How is the perimeter of the circle calculated when it is inscribed in a square with a side length of 10 feet?

• Perimeter = 2π × 10 feet

• Perimeter = π × 10 feet

• Perimeter = π × 20 feet

• Perimeter = π × 5 feet