Question

В трапеции описанной около окружности радиуса 4, разность боковых сторон равна 4, а длина средней линии равна 12.Найдите длины сторон трапеции. Прошу напишите решение. Очень нужно, умоляю

Answer 1

Четырехугольник можно описать вокруг окружности, если суммы противоположных сторон равны. Зная значение средней линии =  12, можно узнать сумму оснований. Она равна 24. Значит, можем составить уравнение, приняв за х - длина боковой стороны, х+4 - длина другой боковой стороны   -   х+(х+4)=24  2х=20   х=10. Узнали боковые стороны - 10 и 14. 

Answer 2

Problem Analysis

We are given a trapezoid inscribed in a circle with a radius of 4. The difference between the lengths of the parallel sides of the trapezoid is 4, and the length of the median line is 12. We need to find the lengths of the sides of the trapezoid.

Solution

Let's denote the lengths of the parallel sides of the trapezoid as a and b, with a being the longer side. The length of the median line is given as 12.

From the problem statement, we know that the difference between the lengths of the parallel sides is 4. Therefore, we can write the equation:

a - b = 4 (Equation 1)

We also know that the median line of a trapezoid is equal to the average of the lengths of the parallel sides. Therefore, we can write the equation:

(a + b) / 2 = 12 (Equation 2)

To solve this system of equations, we can substitute the value of a from Equation 1 into Equation 2:

(4 + b) / 2 = 12

Simplifying this equation, we get:

4 + b = 24

Solving for b, we find:

b = 20

Substituting this value of b back into Equation 1, we can solve for a:

a - 20 = 4

Simplifying this equation, we get:

a = 24

Therefore, the lengths of the sides of the trapezoid are a = 24 and b = 20.

Answer

The lengths of the sides of the trapezoid are 24 and 20.