A friend gave me a puzzle that seems very very tricky to me, and that we couldn't solve so far.
It asks for the minimum size of a pentagon that covers a regular heptagon with sides of length $1$.
It is not neccesary for the polygons to be concentric. What struggles me is that playing with Geogebra the optimal configuration seems very unintuitive to me, and calculations become very ugly. Is it that I am missing something? Maybe there is a closed formula for such minimal length (using sines or cosines of possibly ugly multiples of $\pi$) and I can't get it.