Why can regular polygons be inscribed into a circumference? I have asked this to myself a lot of times. I have also wondered why all triangles can be inscribed into a circumference but I think that it is not so difficult to see why.
I also have another question. Suppose that you have a circumference of radius R and you draw a chord of length L in some direction. And then draw another circumference with the same radius and draw another chord with same length L but in another direction, is it possible to rotate the second figure or apply some transformation to it, so that it looks like the first figure? It might be a silly question but I'd appreciate any answer or help.