Poncelet's Porism

Construct an animation demonstrating Poncelet's Porism for circles: If two circles are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn. |

Modify the above situation to the case when the word "circumscribe" also means the extension of the sides of the triangle circumscribing the circle. |

Construct an animation showing: if two circles are so related that a quadrilateral can be inscribed to one and circumscribed to the other, then there are infinitely many such quadrilaterals can be so drawn. |

Construct an animation showing: if two circles are so related that a quadrilateral can be inscribed to one and circumscribed to the other exteriorly, then there are infinitely many such quadrilaterals can be so drawn. |

Construct an animation demonstrating: If a circle and a parabola are so related that a triangle can be inscribed to one and circumscribed to the other, then there are infinitely many such triangles can be so drawn. |

Construct an animation demonstrating: If a circle and a parabola are so related that a triangle can be inscribed to the parabola and circumscribed to the circle externally, then there are infinitely many such triangles can be so drawn. |

Construct an animation demonstrating: If an ellipse and a parabola are so related that a quadrilateral can be inscribed to the ellipse and circumscribed to the parabola externally, then there are infinitely many such quadrilaterals can be so drawn. |

Construct an animation demonstrating: If two parabolas are so related that a quadrilateral can be inscribed to one and circumscribed to the other externally, then there are infinitely many such quadrilaterals can be so drawn. |

Construct an animation showing if there exists one inscribed "star" of a given ellipse tangent to a fixed ellipse, then there are infinitely many inscribed "stars" of the ellipse having the same property. |