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Circumsphere of a Tetrahedron

Circumsphere of a Tetrahedron
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2020-01-28 01:35
Solid GeometryGeometric Construction
This example demonstrates the circumsphere of a tetrahedron. Key mathematical concepts include solid geometry and spheres. Using GeoGebra commands such as Point, Pyramid, Midpoint, OrthogonalPlane, IntersectPath, Intersect, and Sphere, the circumsphere of a tetrahedron can be constructed. Suitable for high school and above students or teachers.

GeoGebra Commands & Parameters

  1. Point(zAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → C
  4. Point(yAxis) → D
  5. Pyramid(A, B, C, D) → a, faceABC, edgeCD, faceABD, faceBCD, faceACD, edgeAB, edgeBC, edgeAC, edgeAD, edgeBD
  6. Midpoint(B, C) → E
  7. OrthogonalPlane(E, edgeBC) → p
  8. Midpoint(C, D) → F
  9. OrthogonalPlane(F, edgeCD) → q
  10. Midpoint(B, D) → G
  11. OrthogonalPlane(G, edgeBD) → r
  12. IntersectPath(q, r) → f
  13. Midpoint(A, D) → H
  14. OrthogonalPlane(H, edgeAD) → p_1
  15. IntersectPath(p_1, q) → g
  16. Intersect(f, g) → I
  17. Sphere(I, A) → b

AI Drawing Prompt Reference

Draw the circumsphere of a tetrahedron. Start by placing four points A, B, C, and D on the coordinate axes to form a tetrahedron. Then find the midpoints E, F, and G of edges BC, CD, and BD, and construct planes perpendicular to these edges. Find the intersection line f of planes p and q, and the intersection line g of planes q and p_1. The intersection point I of lines f and g is the center of the circumsphere. Finally, draw the circumsphere b with I as the center and A as the radius.
The prompt above was compiled from the original drawing commands and is for reference only.