Question

Дано два рівні кола з центрами О і О, які не мають спільних точок, ОО, = 10 см. Пряма і паралельна ОО, і перетинає ці кола послідовно в точках А, В, С і Д. Знайдіть довжину відрізка АС.

Answer 1

Ответ:

Спочатку знайдемо відстань між центрами колів ОА:

ОА = ОО, - АО = 10 - 5 = 5 см (де 5 см - радіус кола).

Оскільки пряма АВ паралельна ОО, і проходить через центри колів, то АВ - діаметр кола ОВ.

Отже, ОВ = АВ = 2 * 5 = 10 см.

Далі, знову віднімаємо радіуси колів від відстані між центрами, щоб знайти довжину відрізка СD:

ОС = ОО, - АО = 5 см.

ОС = ОВ - ВС = 10 - 5 = 5 см.

Тож СD = ОС - СО = 5 - 5 = 0.

Отже, точки С і D співпадають, тому відрізок АС - це діаметр кола ОА і його довжина:

АС = 2 * 5 = 10 см.

Відповідь: 10 см.

Answer 2

Problem Analysis

We are given two concentric circles with centers O and O', which do not have any common points. The distance between the centers, OO', is 10 cm. There is a line that is parallel to OO' and intersects the circles at points A, B, C, and D. We need to find the length of segment AC.

Solution

To find the length of segment AC, we need to determine the radius of the larger circle and the distance between points A and C.

Let's denote the radius of the larger circle as R and the radius of the smaller circle as r.

Since the line is parallel to OO', the distance between the line and the center of the larger circle is equal to the radius of the larger circle (R). Similarly, the distance between the line and the center of the smaller circle is equal to the radius of the smaller circle (r).

We can form a right triangle with the line segment AC as the hypotenuse. The legs of the triangle are the difference between the radii of the two circles (R - r) and the distance between the centers of the circles (OO').

Using the Pythagorean theorem, we can find the length of segment AC:

AC^2 = (R - r)^2 + OO'^2

To find the radius of the larger circle (R), we can use the fact that the distance between the centers of the circles (OO') is equal to the sum of the radii of the two circles (R + r):

OO' = R + r

Solving these two equations simultaneously will give us the values of R and r. Once we have the values of R and r, we can substitute them into the equation for AC to find its length.

Let's calculate the length of segment AC step by step.

Calculation

1. We are given that OO' = 10 cm. 2. We know that OO' = R + r, where R is the radius of the larger circle and r is the radius of the smaller circle. Therefore, R + r = 10 cm. 3. We need to find the value of R - r to calculate AC. Unfortunately, we don't have enough information to determine the individual values of R and r. 4. Without additional information, we cannot determine the exact length of segment AC.

Conclusion

Based on the given information, we cannot determine the exact length of segment AC without additional information.