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**Various Forms of Poncelet's Porism**

**Constructions with the
Compass Alone**

**Constructions with
the Ruler Alone**

Conic | Midpoint of a Line Segment, Given a Parallel Line |

Parallel through a Given Point, Given the Midpoint | ¡@ |

**Double Generation**

**Dissection**

Dissection of a Disk | Dissection of One Square Into Three Squares |

Dudeney's Trick | Decomposition of Acute Triangles into Similar Pieces |

**Epicycloids
and Hypocyloids-Basic Constructions**

**Epicycloids
and Hypocyloids-Various Properties**

**Curves as Envelope of Tangents**

**Osculating Circle and Involuate**

Schroeter's Construction of Regular Pentagon | Regular Pentagon |

Regular Pentagon | Inscribing a Square In a Regular Pentagon |

Pentagon Determined by the Midpoints of its Sides | ¡@ |

**Steiner's Porism**

Steiner's Porism | Steiner's Porism |

Steiner's Porism-Basic Case | Steiner's Porism |

Degenerate Case of Steiner's Porism | Degenerate Case of Steiner's Porism |

**Parabola**

**Radical Axes**

Radical Axes-Property 1 | Radical Axes-Property 2 |

Radical Axes-Property 3 | Radical Axes-Property 4 |

Radical Axes-Property 5 | ¡@ |

**Squares**

Colinearity | Colinearity |

Colinearity | Neuberg's Theorem |

Square Dance | Square Passing Through Four Given Collinear Points |

**Coaxal System**

Coaxal System | Coaxal System |

Coaxal System | Coaxal System |

Coaxal System | Apollonius Circles |

Tangents at Collinear Points | ¡@ |

**Invariant Properties**

**Duality**

**Circles**

**Triangle**

**Conics**

**Curves**

Chebyshev Polynomials | Chebyshev Polynomial |

Bowditch Curve | Cubic Interpolation Polynomial |

Gerono Lemniscate | Witch of Agnesi |

Conchoid of Nicomedes | Egg |

Freeth's Nephroid | Pearl |

**Quadrilateral**

Quadrilateral in and Quadrilateral about a Cricle | Centers of Gavity of Triangles |

Every Quadrilateral May be Projected into a Parallelogram | ¡@ |

**Seven Circles Theorem**

Degenerate Case | Seven Circles Theorem |

Degenerate Case | Degenerate Case |

Degenerate Case | Degenerate Case |

Degenerate Case | Degenerate Case |

**Unsorted**