Recently, there was a post looking at how to use the relationships of segments that are tangent to a circle to calculate more than just congruence.  Somewhere, and I’m not sure where, I remember Regan Galvan putting out there a tweet/post/comment about tan-tan angles on a clock.  Upon searching for it I found this:

I wanted to know how this thing worked.  So I built my own.

I purposely left out a lot of the information. I didn’t give any measures for angles or segments. This would be something that is developed in the classroom. The user and/or facilitator should be developing questions like:

• How do I measure the angle between the clock hands?
• How far away is the intersection point?
• Is the intersection point always outside the circle?
• What time is it when the two hands are perpendicular?
• What time is it when the two hands are opposite rays?
• Besides 12:00, what time is it when the two hands overlap?

Getting students to investigate these and asking to show evidence and create an argument to support their claim would be so much more fun than just calculating pre-made samples.  For students wanting more feedback and support, they can use the visnos interactive application.