Question

Радіус кола з центром у точці А дорівнює 9 см, а радіус кола с центром у точці В 2 см, знайдіть відстань між центрами цих кіл​

Answer 1

Ответ:

11 см

Пошаговое объяснение:

Answer 2

Calculating the Distance Between the Centers of Two Circles

To find the distance between the centers of two circles with radii 9 cm and 2 cm, we can use the distance formula. The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

Distance Formula: \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

In this case, we can consider the centers of the circles as the points \((x_1, y_1)\) and \((x_2, y_2)\). Let's calculate the distance using this formula.

Calculating the Distance

Given: - Radius of circle with center at point A = 9 cm - Radius of circle with center at point B = 2 cm

We need to find the distance between the centers of these circles.

Using the distance formula, the distance between the centers of the circles can be calculated as follows:

\[d = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2}\]

Where: - \(x_A\) and \(y_A\) are the coordinates of the center of circle A - \(x_B\) and \(y_B\) are the coordinates of the center of circle B

Applying the Given Radii

Since the radii of the circles are given, we can assume that the centers of the circles are located at the points \((0, 0)\) for circle A and \((0, r_A + r_B)\) for circle B, where \(r_A\) and \(r_B\) are the radii of circles A and B, respectively.

Substituting the given values: - \(r_A = 9\) cm - \(r_B = 2\) cm

We can calculate the distance between the centers of the circles using the distance formula.

Calculation

\[d = \sqrt{(0 - 0)^2 + (0 - (9 + 2))^2}\] \[d = \sqrt{0^2 + (-11)^2}\] \[d = \sqrt{0 + 121}\] \[d = \sqrt{121}\] \[d = 11\]

So, the distance between the centers of the circles is 11 cm.

This calculation is based on the given radii and the distance formula, and it yields a distance of 11 cm between the centers of the circles.