J for Japanese Theorem (A to Z challenge)

Well this is embarassing... I must not know my alphabet!  I accidentally skipped J.  I think I was so excited to do my giveaway with my kidsmathteacher as the K that I repressed my knowledge of the alphabet : )

Make sure to enter my giveaway that I posted about yesterday with three great prizes!

For a real stretch for elementary school kids you can show them that there are problems that take multiple steps to solve--theorems.  A problem with all the steps completed make up a theorem.  There is a theorem in geometry called the 'Japanese Theorem' (Thanks Wolfram mathworld for having an alphabetical glossary and explaining things simply).

This theorem states that if you draw the same circle but make triangles in the interior in any manner, then draw incircles to those triangles, the sum of the interior radiuses will always be the same (even if your triangles don't look the same as the others).

Original picture on http://mathworld.wolfram.com

It is pretty neat!  I tried to make my own, but making the incircles is harder than you might think to make sure it barely touches.  I think these look pretty neat and even in kids don't know exactly how to do it, just seeing this makes you curious more about math, right?

'Til Monday!  Have a great weekend!