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Lesson 10.4 Inside Intersection

Lesson 10.4 Inside Intersection
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2018-04-11 09:45
TriangleCircleGeometric Construction
This example demonstrates the geometric relationship between the incircle and intersection points within a triangle. It involves core concepts like intersection, logarithmic functions, incircle or inscribed circle, median value, logic, and cubes. The construction uses commands such as Circle, Point, Line, OrthogonalLine, Intersect, CircleArc, Angle, CircumcircleArc, Vector, and Segment. Suitable for high school and above, it helps learners understand complex geometric constructions and function applications.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Line(drag, C) → a
  4. OrthogonalLine(C, a) → b
  5. Circle(C, drag) → d
  6. Intersect(d, b, 2) → E
  7. Intersect(d, b, 1) → F
  8. CircleArc(C, E, drag) → e
  9. CircleArc(C, drag, F) → f
  10. Point(e) → G
  11. Point(f) → H
  12. Line(G, C) → g
  13. Line(H, C) → h
  14. CircleArc(C, G, H) → k
  15. Angle(G, C, H) → α
  16. Intersect(c, g, 2) → I
  17. Intersect(c, h, 2) → J
  18. Intersect(c, a, 2) → K
  19. CircumcircleArc(I, K, J) → p
  20. OrthogonalLine(G, g) → i
  21. Point(i) → D
  22. Vector(D, G) → u
  23. OrthogonalLine(H, h) → j
  24. Point(j) → L
  25. Vector(L, H) → v
  26. Segment(I, A) → l
  27. Segment(A, J) → m
  28. Angle(I, A, J) → β

AI Drawing Prompt Reference

Start with a large circle and pick a point on it. Draw a tangent line through that point, then create a smaller circle centered at the same point, intersecting the tangent at two points. Use these two points to define two arcs on the small circle, and place a point on each arc. Connect these points to the center, forming two radial lines. Between these lines, draw an arc on the small circle and mark its angle. Extend the radial lines to meet the large circle, giving two intersection points. Together with another point on the large circle, draw an arc through these three points. Then construct perpendiculars to the radial lines, place points on them, and draw vectors from those points to the arc points. Finally, connect the two large-circle intersections with the initial point to form a triangle, and label its vertex angle.
The prompt above was compiled from the original drawing commands and is for reference only.