There are two circles with radii 2 and 6. The centers of the circles are 10 units apart. What is the distance between the two tangency points as seen in the diagram?
Let's call the centers of the circles A and B, and let the tangency points be C and D, as shown in the diagram below:
Since the radii of the circles are 2 and 6, AC=2 and BD=6. Also, AB=10, since the centers of the circles are 10 units apart.
Triangle ABD is a right triangle, so by the Pythagorean Theorem, AD=AB2−BD2=102−62=64=8.
Therefore, the distance between the two tangency points C and D is 8 units.