How do I proove that a regular octagon has a centre?
By centre i mean a point equidistant from all the vertices?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this community
Take a line segment from one vertex to its opposite vertex. Bisect that segment. Clearly this point is equidistant from those two vertices.
Now rotate the octagon about that point, placing two new vertices onto the ends of the line segment. Rotations don't change distance; so those two vertices must be equidistant from the centre too.