Question

Две окружности касаются внешним образом. Радиус одной окружности на 3 см меньше радиуса другой окружности. Найдите диаметры окружностей, если расстояние между их центрами равно 11 см. Решите срочно!!!!!!!!

Answer 1

Пусть x - радиус большей окружности, а х-3 - радиус меньшей окружности.

Получаем уравнение:

x + x - 3 = 11

2x = 14

x = 7 ( радиус большей окружности)

Знаем, что диаметр больше радиуса в два раза, тогда d=2r, то есть d=14

Радиус меньшей окружности  равен 4, так как 7 - 3 = 4

А диаметр соответсвенно равен 8

Ответ: 14 cм и 8 см 

Answer 2

Problem Analysis

We are given two circles that touch externally. The radius of one circle is 3 cm less than the radius of the other circle. The distance between their centers is 11 cm. We need to find the diameters of the circles.

Solution

Let's assume the radius of the larger circle is R cm. Therefore, the radius of the smaller circle will be R - 3 cm.

The distance between the centers of the circles is given as 11 cm. This distance is equal to the sum of the radii of the two circles.

Using the Pythagorean theorem, we can form the following equation:

R + (R - 3) = 11

Simplifying the equation, we get:

2R - 3 = 11

Solving for R, we find:

2R = 14

R = 7

Therefore, the radius of the larger circle is 7 cm, and the radius of the smaller circle is 4 cm.

The diameter of a circle is twice its radius. So, the diameter of the larger circle is 2 * 7 = 14 cm, and the diameter of the smaller circle is 2 * 4 = 8 cm.

Answer

The diameter of the larger circle is 14 cm, and the diameter of the smaller circle is 8 cm.