Step-back SAT/GRE problems -- trying something new at "You Do the Math"

I've been thinking about the problem of adapting lessons for different media in general and for video in particular. There is a popular but wildly misguided impression that you can create an effective video by just sticking a camera in front of a live presentation. Teaching live is an interactive process. Even when the students don't say a word, the good teacher is alert to the class's reactions. You speed up, slow down, offer words of encouragement, come up with new examples and occasionally stop what you're doing and go back and reteach a previous section.

With a video lesson you set the course then you leave the room. What's worse, it's a really big room and many if not most of the kids are there because the standard methods of instruction have not served them well.

One idea I'm playing with is thinking of the problems in terms of a graph (as in graph theory, not data visualization) where the path is determined by how well the student is doing. As a start in that direction I'm playing around with paired problems -- if you are confused by the first (more difficult) problem there an easier one to try -- and I've got the first couple up at the teaching blog.

Here's the medium problem:

Circle 1

The radius of circle 1 is 5. Both line segments pass through the center of the circle. Find the area of the shaded region.


You can find the answer and explanation at You Do the Math. Feedback is always appreciated.