MathDB

10

Part of 1998 Baltic Way

Problems(1)

Inscribed n-gon and n-1-gon

Source: Baltic Way 1998

1/11/2011
Let n≥4n\ge 4 be an even integer. A regular nn-gon and a regular (n−1)(n-1)-gon are inscribed into the unit circle. For each vertex of the nn-gon consider the distance from this vertex to the nearest vertex of the (n−1)(n-1)-gon, measured along the circumference. Let SS be the sum of these nn distances. Prove that SS depends only on nn, and not on the relative position of the two polygons.
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