MathDB
Obtuse-Angled n-gon

Source: Turkey TST 2016 P8

April 10, 2016
geometrycircumcirclepolygon

Problem Statement

All angles of the convex nn-gon A1A2…AnA_1A_2\dots A_n are obtuse, where n≥5n\ge5. For all 1≤i≤n1\le i\le n, OiO_i is the circumcenter of triangle Ai−1AiAi+1A_{i-1}A_iA_{i+1} (where A0=AnA_0=A_n and An+1=A1A_{n+1}=A_1). Prove that the closed path O1O2…OnO_1O_2\dots O_n doesn't form a convex nn-gon.
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