A Challenging Problem...

I encourage you to visit jd2718 and the stimulating discussion over the 'innocent-looking' geometry problem he posed. Read the comments below the problem. I struggled with this problem myself, shared it with my department and ended up constructing the counterexample using traditional tools, not Geometer's Sketchpad! The author of this excellent blog made a compelling point about our need to struggle with difficult problems ourselves as math educators. It's not only humbling, but reminds us of the need for our students to be similarly challenged. Most mathematical geniuses had inspiration but they had the one quality that separated them from the rest -- they didn't give up. Just ask Professor Wiles from Princeton!

By the way, there's another challenge geometry problem there today involving 3 circles. Guess I'm going to lose more sleep...