TwoFamiliesPonceletTriangles(Hyperbola)::usage=" Poncelet's porism says that a polygon is inscribed in a conical and circumscribes another, the polygon must be part of an infinite family of polygons that are all inscribed and circumscribe the same two conicals. References: Wolfram MathWorld: Poncelet's Porism; YouTube: Exploring the Dynamic Geometry and Conservations of the Steiner-Soddy and Harmonic Poncelet Porism, Dan Reznik; Personal ";
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The circumference that passes through the tangent points of the circumferences of the Steiner chain, is exinscribed to the family of polygons 1 (in orange) whose vertices are the centers of the circles of the Steiner chain and are located on a hyperbola. The family of polygons 2 (in dark green) is inscribed on that circle and its vertices are the tangential points between the circles of the Steiner chain.