Alternate segments theorem

First, students will learn what the alternate segments theorem is, and how to use it.

Next, students will see two proofs of the alternate segments theorem.

Conclude by giving your students this challenge: In the figure below, the radius of each large circle is 4. What's the radius of the small circle?

The only prereq is knowing that the centers and point of contact for touching circles are collinear. Here's the solution.