How do I proove that a regular octagon has a centre?
By centre i mean a point equidistant from all the vertices?
2026-04-28 16:27:55.1777393675
Proof that a regular octagon has a centre
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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.
Repeat.