Елипса на Понселе-Лемоан за триъгълник, който се движи между две фиксирани окръжности
Pfncelet-Lemoine ellipse for a triangle, moving between two fixed circles

Summary/Abstract: According to a remarkable theorem belonging to the French mathematician Poncelet, if two circles Г и ω could be located in the plane in such a way that Г is circumscribed with respect to a triangle and ω is inscribed in it, then each point from Г is a vertex of a triangle which is inscribed with respect to Г and circumscribed with respect ω. In case of such a location of Г и ω in the plane it is possible for a tringle to move constantly inscribed with respect to Г and circumscribed with respect to ω. Along the movement between the two fixed circles the notable points of the triangle describe determined loci. A locus is considered in the present paper which is described by the Lemoine point in the plane of the moving triangle. It turns out that the locus in question is an ellipse with center on the central line of the fixed circles. This circle is called Poncelet-Lemoine circle.

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