Question

Длинна средней линии равнобедренной трапеции, описанной около круга, равна 17 см, а одно из оснований меньше первого на 16 см. Найти радиус круга.

Answer 1

Меньшее основание трапеции равно 17 - 8 = 9 см, тогда большее равно 9+16 = 25 см.

Если рапеция описана возле круга. то длина боковой стороны равна (9+25 = 34)/2 = 17.

Высота трапеции равна корню квадратному из  289 - 64 = 225, т.е. 15.

Тогда радиус окружности равен 15/2 = 7,5.

 

Ответ: 7,5

Answer 2

17-8=9 см,9+16=25 см,9+25=34/2=17288-64=225,15/2=7,5 ответ 7,5

Answer 3

Calculating the Radius of the Circle

To find the radius of the circle, we can use the given information about the trapezoid and its relationship with the circle.

Given: - Length of the median of the isosceles trapezoid circumscribed around the circle = 17 cm - One of the bases is 16 cm shorter than the other

Let's denote: - Length of the longer base of the trapezoid as b - Length of the shorter base of the trapezoid as b - 16 (since it's 16 cm shorter than the longer base)

The length of the median of the trapezoid can be calculated using the formula: Median = √(2a^2 + 2b^2 - c^2) / 4 where a and b are the lengths of the bases and c is the distance between the bases.

Calculating the Radius

Using the given information, we can calculate the radius of the circle using the formula for the median of the trapezoid.

The formula for the median of the trapezoid can be used to find the radius of the circle.

Using the formula: Median = √(2a^2 + 2b^2 - c^2) / 4

Substituting the given values: 17 = √(2b^2 + 2(b-16)^2 - c^2) / 4

Solving for c: c = √(2b^2 + 2(b-16)^2 - 4*17^2)

This will give us the value of c, which is the radius of the circle.

Let's calculate the value of c using the given information and the formula.