Question

Найдите радиусы окружностей описанной около прямоугольного треугольника а если катеты равны 5см и 11 корней

Answer 1

Гипотенуза этого треугольника будет диаметром описанной окружности, значит радиус равен половине гипотенузы, гипотенузу найдем по т Пифагора с=√(5²+11²)=√(25+121)=√146
значит R=√146/2

Answer 2

Finding the Radii of Circles Circumscribed around a Right Triangle

To find the radii of the circles circumscribed around a right triangle, we need to know the lengths of the triangle's legs. In this case, the lengths of the legs are given as 5 cm and 11 cm.

Let's calculate the radii using the given information.

The radius of the circle circumscribed around the right triangle can be found using the formula:

Radius = (Hypotenuse / 2)

In a right triangle, the hypotenuse is the longest side, and it can be calculated using the Pythagorean theorem:

Hypotenuse = sqrt(leg1^2 + leg2^2)

For the given triangle with leg1 = 5 cm and leg2 = 11 cm, we can calculate the hypotenuse:

Hypotenuse = sqrt(5^2 + 11^2) = sqrt(25 + 121) = sqrt(146) cm

Now, we can calculate the radius of the circle circumscribed around the right triangle:

Radius = (sqrt(146) / 2) cm

Therefore, the radius of the circle circumscribed around the right triangle with legs measuring 5 cm and 11 cm is approximately (sqrt(146) / 2) cm.

Please note that the exact value of the radius will depend on the accuracy of the measurements provided.