Beautiful Geo

For discussing Olympiad level Geometry Problems
Ainur Nishad
Posts:1
Joined:Sun Oct 19, 2014 11:49 pm
Beautiful Geo

Unread post by Ainur Nishad » Sun Oct 19, 2014 11:51 pm

a very beutiful problem:

Let ωP and ωQ be two circles of radius 1, intersecting in points A and B. Let P
and Q be two regular n-gons (for some positive integer n ≥ 4) inscribed in ωP and ωQ,
respectively, such that A and B are vertices of both P and Q. Suppose a third circle ω of
radius 1 intersects P at two of its vertices C, D and intersects Q at two of its vertices E, F.
Further assume that A, B, C, D, E, F are all distinct points, that A lies outside of ω, and
that B lies inside ω. Show that there exists a regular 2n-gon that contains C, D, E, F as
four of its vertices.

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