The distance between the centers of two circles, tangent in an internal way, is 18 cm

The distance between the centers of two circles, tangent in an internal way, is 18 cm. Find the radii of the circles if one of them is 4 times smaller than the other.

To solve the problem, we will compose an equation in which we write the radius of the smaller circle as an unknown value x.

Since we know that the radius of the second circle is 4 times larger, it will be equal to: 4 * x.

In this case, the difference between the radius of the two circles is:

4 * x – x = 18 cm.

3 * x = 18.

x = 18/3 = 6 cm (radius of the smaller circle).

4 * x = 4 * 6 = 24 cm (radius of the larger circle).

Answer:

The radii of the circles are 6 and 24 cm, respectively.