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Tangent and Intersection of a Circle

Tangent and Intersection of a Circle
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2017-03-15 00:02
CircleCoordinate GeometryGeometric Construction
This example demonstrates how to construct the tangent and intersection of a circle using GeoGebra. Key mathematical concepts include the properties of circles, the definition of tangents, and the calculation of intersection points. By using commands such as Intersect, Point, Circle, and Segment, the construction process of geometric figures is vividly illustrated. Suitable for students at the junior high school level and above to learn about coordinate geometry and circle-related knowledge.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Point(yAxis) → Β
  3. Circle(O, Β) → c
  4. Point(c) → Γ
  5. Point(c) → Δ
  6. Intersect(c, xAxis, 2) → A
  7. Segment(O, Δ) → a
  8. Segment(O, Γ) → b
  9. Segment(Γ, Δ) → d
  10. OrthogonalLine(Γ, xAxis) → e
  11. OrthogonalLine(Δ, xAxis) → f
  12. OrthogonalLine(O, d) → g
  13. Intersect(g, d) → Ζ
  14. Intersect(e, xAxis) → Γ_1
  15. Intersect(f, xAxis) → Δ_1
  16. Segment(Γ_1, Γ) → h
  17. Segment(O, Ζ) → i
  18. Segment(Δ, Δ_1) → j
  19. Angle(A, O, Γ) → β
  20. OrthogonalLine(Ζ, xAxis) → k
  21. Intersect(k, xAxis) → Z_1
  22. Segment(Ζ, Z_1) → l
  23. Angle(Ζ, O, Γ) → γ
  24. Angle(A, O, Ζ) → δ
  25. Point(i) → Α
  26. Point(d) → Ε
  27. Ray(O, Ζ) → q
  28. Intersect(c, q, 1) → Η
  29. Segment(Ζ, Η) → r
  30. OrthogonalLine(Η, xAxis) → s
  31. Intersect(xAxis, s) → Θ
  32. Segment(Η, Θ) → t
  33. Angle(A, O, Δ) → α