Семейство окръжности на Понселе-Ойлер за триъгълник, който се движи между две фиксирани окръжности
A family of Poncelet-Euler circles 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 and 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. What are considered in the present paper are loci which are described by the points on the Euler circle of the moving triangle. It turns out that each point on the Euler circle describes a circle which is externally tangent to ω. Such a circle is called Poncelet-Euler circle.

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