converting a n-gon with side length s into a 2n-gon with side length t So I have to prove that  $$ t= \sqrt{2-\sqrt{4-s^2}} $$
If I have a n-gon with side length s inscribed in a unit circle then bisect it to create a 2n-gon with side length t, there should be some relationship, right?
I'm not even sure how to relate them? Area? Sides? Angles? Pythagorean theorem?
I even tried drawing it with compass. No luck. Help?

Hint:
If the angle at the center for the $n-$gon is $2\alpha$ we have:
$$
s=2\sin \alpha \qquad t=\sqrt{(1-\cos \alpha)^2+\sin ^2\alpha}
$$
Calculating $t$ and substituting $s$ you have the result in OP.

$\angle BOA=2\alpha \Rightarrow \angle BOC = \alpha$
$BA=s \qquad BC=t$

