Insphere and Four Exspheres of a Tetrahedron

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A tetrahedron has four vertices and four triangular faces. There are five spheres tangent to all four planes containing the faces.

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A small sphere near a vertex touching three faces inside the tetrahedron can grow until it touches the fourth face: that is the insphere. It can keep growing until it touches the same face on the other side: that is an exsphere. Moving a sphere slider to 1 produces an exsphere.

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Contributed by: George Beck (December 2015)
Open content licensed under CC BY-NC-SA


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