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Improved demonstration of the Poncelet theorem

Poncelet theorem for pentagram
Three-parameter family of pairs of Poncelet conics with the outer being a circumference with in- and circumscribed oentagram are presented in the animation (three parameters with sliders and the point S can be animated). The parameter alpha does not reach its upper limit pi/2 due to some technical difficulties. The pattern moves because in fact the problem is 3-dimensional and I could not find motion of the center.