Two circles are tangent internally. Find the radii of the circles if the distance between

Two circles are tangent internally. Find the radii of the circles if the distance between their centers is 4 dm, and the ratio of the radii is 1: 3

Let’s construct the radii ОА and О1В of the circles.

Distance OO1, by condition, is equal to 4 dm.

Let the radius O1B = X dm, then, by condition, the radius OA = 3 * X dm.

The sum of the radii OA, O1B and segment OO1 is equal to the diameter of the larger circle.

AB = 2 * OA = (OA + OO1 + O1B).

2 * 3 * X = 3 * X + 4 + X.

2 * X = 4.

X = O1B = 4/2 = 2 dm.

Then OA = 3 * 2 = 6 dm.

Answer: The diameters of the circles are equal to 2 dm and 6 dm.