The geometry puzzle reminded me of another site I vistited before -
http://www.ocf.berkeley.edu/~wwu/riddles/intro.shtml
- and some puzzles called
sangaku. For example:
http://www.ocf.berkeley.edu/~wwu/rid...shtml#sangaku1

Find the side length of the internal square and the radii of the internal circles, in terms of a.
(I haven't figured it out, yet. Maybe I'm getting too mathematical here, anyway.)
The berkeley site has a bunch of other puzzles and riddles, though.