Argthtjtr

up vote 11 down vote favorite 3 I'm now working on a geometry problem I'll have to explain in front of my class this week (I'm in the $10^{th}$ grade). I've found so far some proofs, which might, nevertheless, be a bit complicated for my classmates (since they've barely worked with geometry). I was wondering hence, whether there might be a "more elementary" proof or an animation (I don't know how to program it) which somehow makes it clearer or at least visual... The problem is the following Consider a square $ABCD$ with side $[AB]=a$ and a circumference $omega$ with radius $r$ , such that both are "semi inscribed" in each other (the image below might clarify this). Proof that the following relation holds $$a=frac{8r}{5}$$ My proofs so far are the following Con