# Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

Find the exspheres of a triangle or tetrahedron

Contributed by:
Minh Trinh Xuan, Ed Pegg Jr and Jan Mangaldan

ResourceFunction["Exspheres"][{ constructs the excircles of the triangle defined by vertices | |

ResourceFunction["Exspheres"][{ constructs the exspheres of the tetrahedron defined by vertices |

An excircle is also called an escribed circle. An exsphere is also called an escribed sphere.

An incircle is internally tangent to the edges of a triangle. A triangle has three excircles that are externally tangent to each side and to the other sides when extended indefinitely.

An insphere is internally tangent to the faces of a tetrahedron. A tetrahedron has four exspheres that are externally tangent to each face at its incenter and to the other faces when extended indefinitely.

ResourceFunction["Exspheres"][*poly*] where *poly* is a Triangle or Polygon is equivalent to ResourceFunction["Exspheres"][PolygonCoordinates[*poly*]].

ResourceFunction["Exspheres"][*poly*] where *poly* is a Tetrahedron is equivalent to ResourceFunction["Exspheres"][PolyhedronCoordinates[*poly*]].

Find the excircles for a triangle:

In[1]:= |

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Show the excircles, incircle and infinite lines:

In[3]:= |

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A triangle:

In[4]:= |

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Show the triangle along with its excircles:

In[5]:= |

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Show a tetrahedron along with its exspheres:

In[6]:= |

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Show the insphere and exspheres of a regular tetrahedron:

In[7]:= |

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Show the excircles of an arbitrary triangle:

In[8]:= |

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A triangle and its excircles:

In[9]:= |

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Compute the center and the radius of the radical circle of the excircles:

In[11]:= |

Show the triangle, its excircles and the radical circle altogether:

In[12]:= |

Out[12]= |

- 1.0.0 – 11 July 2022

This work is licensed under a Creative Commons Attribution 4.0 International License