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Italian Mathematical Olympiad 2008

Source: Problem 1

August 23, 2008
geometrycircumcirclegeometry proposed

Problem Statement

Let ABCDEFGHILMN ABCDEFGHILMN be a regular dodecagon, let P P be the intersection point of the diagonals AF AF and DH DH. Let S S be the circle which passes through A A and H H, and which has the same radius of the circumcircle of the dodecagon, but is different from the circumcircle of the dodecagon. Prove that: 1. P P lies on S S 2. the center of S S lies on the diagonal HN HN 3. the length of PE PE equals the length of the side of the dodecagon
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