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Incircle, Excircle, Dandelin Spheres, Ellipse, and Foci

Incircle, Excircle, Dandelin Spheres, Ellipse, and Foci
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2018-04-03 21:05
CircleTrigonometrySolid GeometryGeometric Construction
This example demonstrates the geometric relationships between incircles, excircles, Dandelin spheres, ellipses, and foci. It involves core concepts such as circles, ellipses, geometric construction, solid geometry, and trigonometry. The construction utilizes GeoGebra commands and objects like points, rays, reflections, segments, angle bisectors, intersections, orthogonal planes, path intersections, polygons, orthogonal lines, circles, centers, cones, planes, corners, and spheres. Suitable for high school and above learners to understand the geometric properties of ellipses and related constructions.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Ray(A, B) → f
  3. Mirror(A, yAxis) → A'
  4. Mirror(B, yAxis) → B'
  5. Ray(A', B') → f'
  6. Point(f') → C
  7. Segment(C, B) → g
  8. AngularBisector(C, B, A) → h
  9. Intersect(yAxis, h) → D
  10. OrthogonalPlane(B, h) → a
  11. IntersectPath(xOyPlane, a) → i
  12. Intersect(yAxis, i) → E
  13. Polygon(A, C, B) → t1, b, a_1, c
  14. OrthogonalPlane(D, a_1) → d
  15. OrthogonalPlane(E, a_1) → e
  16. Intersect(a_1, d) → F
  17. Intersect(a_1, e) → G
  18. OrthogonalLine(D, xOyPlane) → j
  19. OrthogonalLine(E, xOyPlane) → k
  20. Circle(k, G) → p
  21. Circle(j, F) → q
  22. Point(f') → H
  23. Circle(yAxis, H) → r
  24. Center(r) → I
  25. Cone(I, A, abs(x(H))) → l, s, m
  26. OrthogonalLine(C, t1) → n
  27. Plane(B, n) → o
  28. IntersectPath(o, l) → t_1
  29. Corner(t_1)
  30. Sphere(E, G) → u
  31. Sphere(D, F) → v