1963 IMO Problems/Problem 3
In an -gon all of whose interior angles are equal, the lengths of consecutive sides satisfy the relation
Prove that .
Define the vector to equal . Now rotate and translate the given polygon in the Cartesian Coordinate Plane so that the side with length is parallel to . We then have that
But for all , so
for all . This shows that , with equality when . Therefore
There is equality only when for all . This implies that and , so we have that .
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