All the angles of a convex octagon are equal, and all of its sides have a rational length. How can I prove that such an octagon has a symmetry center?
First of all, I think we should start with finding the point. Then we can prove that it is a symmetry center. We can easily get the angle measure of each octagon angle: it will be equal to $135$ degrees. Maybe the symmetry point is the bisector intersection point? Currently I do not understand where we should use the fact about rational sides and what would change if the sides were irrational. Maybe this fact should be used in the proof?