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Section of a Cone

Section of a Cone
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2019-05-24 02:12
Solid GeometryGeometric Construction
This example demonstrates the section of a cone. Key mathematical concepts include cones, right triangles, and solid geometry. Using GeoGebra commands such as Circle, Cone, IntersectPath, etc., the section of a cone can be constructed. Suitable for high school geometry lessons.

GeoGebra Commands & Parameters

  1. Circle(B, 3, zAxis) → c
  2. Cone(B, O, 3) → a_2, d, b
  3. OrthogonalLine(C, xOyPlane) → e
  4. Point(e) → D
  5. Vector(C, D) → u
  6. OrthogonalPlane(D, e) → f
  7. IntersectPath(f, a_2) → g
  8. Corner(g)
  9. Intersect(zAxis, f) → E
  10. Point(g) → F
  11. Polygon(E, F, O) → poly1, a, s, h
  12. Line(O, F) → i
  13. Intersect(i, c) → A,
  14. Segment(E, B) → j
  15. Segment(A, B) → k
  16. Segment(F, A) → l

AI Drawing Prompt Reference

Draw a 3D cone with a horizontal circular base and its apex directly above the center. From a point on the base circle, construct a vertical line perpendicular to the base plane. Choose a point on this line, then create a plane through that point perpendicular to the line. This plane intersects the cone's lateral surface, producing a section curve. Connect the apex, a point on the section curve, and the base center to form a triangle. Draw the triangle's edges, a segment from the base center to the section point, and mark where this segment meets the base circle.
The prompt above was compiled from the original drawing commands and is for reference only.