Let A,B,C,D be four points on a circle. Construct four circles S_{1},
S_{2}, S_{3}, S_{4} so that S_{1} is tangent to S_{2}
at A, S_{2} is tangent to S_{3} at B, S_{3} is tangent to S_{4}
at C, S_{4} is tangent to S_{1} at D. |

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Construct the graph of the quadratic polynomial given by a tangent, the point of contact and a second point of the graph. |

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Let A,B,C,D be four points on the graph of a quadratic polynomial.
Construct four quadratic polynomials with graphs S_{1}, S_{2}, S_{3},
S_{4} so that S_{1} is tangent to S_{2} at A, S_{2}
is tangent to S_{3} at B, S_{3} is tangent to S_{4} at C, S_{4}
is tangent to S_{1} at D. |

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Construct the parabola given by two tangents and points of contact. | |

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Construct the common tangents of a parabola and its directrix. |

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Construct the graph of the cubic polynomial p with p(a), p'(a), p(b), p'(b) given. |

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Construct the cubic spline passing through four points. |

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Construct an animation displaying two tangential parabolas, one stationary one moving. |