Two circles are tangent externally. The radius of one circle is 3 times the other.

Two circles are tangent externally. The radius of one circle is 3 times the other. Find their diameters if the distance between their centers is 6 cm.

1. Let x cm be the radius of the smallest circle. Find the radius of the other circle.

x * 3 = 3x cm radius of another circle.

2. Find the distance between their centers.

x + 3x = 4x cm distance between centers.

3. By condition, the distance between the centers is 6 cm.

Let’s compose and solve the equation.

4x = 6;

x = 6/4;

x = 1.5.

4. The radius of the smaller of the circles is 1.5 cm, then the radius of the larger

1.5 * 3 = 4.5 cm.

5 .. Find the diameters of the circles.

1.5 * 2 = 3 cm smaller diameter.

4.5 * 2 = 9 cm larger diameter.

Answer: 3 cm; 9 cm.