Question

3.Два кола з центрами в точках 1 і О, та радіусами 43 см і 12 см дотикаються зовнішньо. Знайти відстань Овог мiж центрами кіл?​

Answer 1

To find the distance between the centers of the two circles, we can use the fact that the circles are externally tangent to each other.

Let's denote the center of the larger circle as A and the center of the smaller circle as B. The radii of the circles are given as 43 cm and 12 cm, respectively.

The distance between the centers of the circles can be found by adding the radii of the two circles and the distance between the points where the circles touch externally.

Let's denote the distance between the centers of the circles as d.

Using the Pythagorean theorem, we can find the distance between the points where the circles touch externally.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the hypotenuse is the distance between the centers of the circles (d), one side is the radius of the larger circle (43 cm), and the other side is the radius of the smaller circle (12 cm).

We can set up the following equation:

d^2 = (43 cm + 12 cm)^2

Simplifying the equation:

d^2 = 55 cm^2

Taking the square root of both sides:

d = √(55 cm^2)

Calculating the value:

d ≈ 7.416 cm

Therefore, the distance between the centers of the two circles is approximately 7.416 cm.