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