Question

Прямоугольный треугольник с катетами 12 см и 16 см вписан в окружность .Найдите его радиус.Если можно решение по подробнее

Answer 1

Радиус описанной окружности прямоугольного треугольника равен половине гипотенузы
по т .Пифагора найдем гипотенузу
$12^{2} + 16^{2} = x^{2}$
$144+256= x^{2}$
$x^{2} =400$
х=20
 поэтому R=10

Answer 2

Problem Analysis

We are given a right triangle with the lengths of its legs (or catheti) as 12 cm and 16 cm. The triangle is inscribed in a circle. We need to find the radius of the circle.

Solution

To find the radius of the circle, we can use the relationship between the radius and the hypotenuse of a right triangle inscribed in a circle. In this case, the hypotenuse of the right triangle is the diameter of the circle.

Let's denote the radius of the circle as R and the hypotenuse of the right triangle as c.

According to the properties of a right triangle inscribed in a circle, the diameter of the circle is equal to the hypotenuse of the right triangle. Therefore, we have:

c = 2R We can use the Pythagorean theorem to find the length of the hypotenuse c:

c^2 = a^2 + b^2 where a and b are the lengths of the legs of the right triangle.

Substituting the given values, we have:

c^2 = 12^2 + 16^2

Simplifying, we