Окръжности, породени от точките върху четири забележителни прави за триъгълник, който се движи между две фиксирани окръжности
Circles, generated by the points on four notable lines for a triangle, moving between two fixed circles

Summary/Abstract: According to a remarkable theorem of the French mathematician Pocelet, if two conics are in such a position in the plane, that a polygon exists, inscribed in one of the curves and circumscribed in the other one, then each point on any of the curves generates a polygon inscribed and circumscribed for the conics under consideration. In a particular case two circles could be positions in the plane in such a way, that one of them is circumscribed for a triangle, while the other one is inscribed for the triangle. In connection with this configuration when the triangle moves between the two circles, some loci are considered of remarkable points in the triangle plane and the points on the remarkable lines which are determined by them. It turns out that all loci under consideration are circles with centers on the central line of the two fixed circles.

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