- 1). Draw a line connecting the radius of the smaller circle to the larger circle. For example, if one circle has a radius of 15 inches and the other circle has a radius of 20 inches, connect the two circles at the 15-inch point. If you do this correctly, you will have a rectangle on your paper. The line you just drew and the tangent line make the long edges of the rectangle, and the radius of the smaller circle and part of the radius of the larger circle make the short edges.
- 2). Label the line you just drew with its length. Its length is the same as the length of the tangent connecting the top of the circles.
- 3). Draw another line connecting the two radii. This line represents the distance between the two circles. By drawing this line, you make a triangle underneath the rectangle, made up of the center line, the line connecting the radii and a short side. Subtract the radius of the smaller circle from the radius of the larger circle to determine the length of the short side. For example, if the radius of the larger circle is 15 inches and the radius of the smaller circle is 10 inches, the length of the short side of your triangle is 5 inches.
- 4). Use the formula A^2 + B^2 = C^2 to determine the length of the line connecting the two radii. Let A equal the line connecting the circles at their center and B equal the length of the short side of the triangle. Using the example of the two circles with a length of 15 inches and 10 inches, if the length of the center line is 30 inches, you would use the formula 30^2 + 5^2 = C^2.
- 5). Solve for C to determine the distance between the circles. In the example above, C^2 = 925 inches, so C = 30.413 inches.
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