Gotta love this question!!! However, I don't know how to explain it well without a drawing. On your paper, draw a sketch of the two circles, one bigger than the other, and touching at one and only one point.
The distance between the centers of the circle is the sum of the radii or 5 + 8 or 13.
Now draw a line segment from each center to the tangent point on the tangent line and on the relevant circle. The length of the shorter segment, which is a radius of the smaller circle, is 5. The length of the longer segment, which is a radius of the larger circle, is 8. Put those lengths on your drawing.
You will notice that you have a shape with two right angles. Connect the two tangent points, A and B, to create a quadrilateral.
Now, draw a line segment that connects the side that is 5 and the side that is 8 and is parallel to the side that is 13. This creates a rectangle. What we are interested in is the right triangle above the rectangle. That right triangle has a long leg of 13 and a short leg of (8 — 5) = 3.
Now, you are almost done! You just need to find the length of the hypotenuse of that right triangle by using the Pythagorean Theorem.
32 + 132 = c2
c will be the distance that you were asked to solve, the distance between points A and B. I will let you have the satisfaction of solving for c. Good luck, Brianna! Geometry requires creativity! Stay with it and develop YOUR creativity!
