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Tetrahedron with a Sphere Inside

Tetrahedron with a Sphere Inside
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2019-01-10 08:08
PolygonSolid GeometryGeometric Construction
This example demonstrates the geometric construction of a sphere inscribed within a tetrahedron, involving key mathematical concepts such as solid geometry, polygons, spheres, triangles, and point-line-plane relationships. The construction utilizes GeoGebra commands like Intersect, Point, Tetrahedron, Plane, OrthogonalLine, Sphere, Segment, and Midpoint. It is suitable for high school geometry instruction or mathematical exploration groups.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → A
  2. Point(xAxis) → B
  3. Point(Circle[Midpoint[A, B], (Distance[A, B] * sqrt(3) / 2), Segment[A, B]]) → C
  4. Tetrahedron(A, B, C) → a, D, edgeCD, edgeBD, faceABC, faceACD, faceABD, faceBCD, edgeAC, edgeAB, edgeBC, edgeAD
  5. Plane(D, A, B) → b
  6. OrthogonalLine(C, b) → f
  7. OrthogonalLine(D, xOyPlane) → g
  8. Intersect(f, g) → E
  9. Intersect(f, b) → F
  10. Sphere(E, F) → c
  11. Segment(F, E) → h
  12. Intersect(g, c) → H, I
  13. Midpoint(edgeBC) → J
  14. Segment(H, J) → k
  15. Segment(H, C) → l
  16. Segment(E, C) → m
  17. Segment(E, J) → n