Question

ХЕЛП!!!!прямокутний трикутник з катетами 5 см і 12 см вписано в круг. знайти площу круга​

Answer 1

Ответ:

Объяснение:

Находим гипотенузу:

c² = a² + b² = 144 + 25 = 169 ⇒ c = 13 см

Так как треугольник прямоугольный, то его гипотенуза - это диаметр окружности, описанной около треугольника.

Тогда S = πd²/4 = 169π/4 см²

Answer 2

Finding the Area of the Circle

To find the area of the circle in which a right triangle with side lengths of 5 cm and 12 cm is inscribed, we can use the fact that the hypotenuse of the right triangle is equal to the diameter of the circle.

The formula for the area of a circle is given by:

Area = π * r^2

where π is a mathematical constant approximately equal to 3.14159, and r is the radius of the circle.

In this case, the diameter of the circle is equal to the hypotenuse of the right triangle, which can be found using the Pythagorean theorem:

c^2 = a^2 + b^2

where c is the hypotenuse and a and b are the lengths of the other two sides of the right triangle.

Let's calculate the hypotenuse first:

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

Taking the square root of both sides, we find:

c = √169

c = 13

So, the diameter of the circle is 13 cm, and the radius is half of the diameter, which is 6.5 cm.

Now, we can calculate the area of the circle:

Area = π * r^2

Area = 3.14159 * (6.5)^2

Area ≈ 132.7324 cm^2

Therefore, the approximate area of the circle is 132.7324 square centimeters.

Please note that the value of π used here is an approximation, and the actual value of π extends to many decimal places.