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?

rb2919 Dec 13, 2023

#4**0 **

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.

Boseo Dec 18, 2023