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Miklós Schweitzer 2007 Problem 9

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March 3, 2017
Miklos Schweitzergeometry

Problem Statement

Let AA and BB be two triangles on the plane such that the interior of both contains the origin and for each circle CrC_r centered at the origin ∣Cr∩A∣=∣Cr∩B∣|C_r \cap A|=|C_r\cap B| (where ∣⋅∣|\cdot | is the arc-length measure). Prove that AA and BB are congruent. Does this statement remain true if the origin is on the border of AA or BB?
(translated by Miklós Maróti)
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