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Tangent-Chord Angles by Arthur Lee

Tangent-Chord Angles by Arthur Lee
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2013-04-20 20:36
CircleAngleGeometric Construction
This example demonstrates the angles formed between a tangent and a chord in a circle, illustrating the ratio of the arcs intercepted by these angles. Key mathematical concepts include circle, tangent line, chord, angle, and arc. Construction involves using GeoGebra commands such as Line, OrthogonalLine, LineBisector, Intersect, Circle, Point, Segment, Angle, Ray, Mirror, and CircleArc. Suitable for high school students studying circles and trigonometric functions.

GeoGebra Commands & Parameters

  1. Line(P, R) → a
  2. OrthogonalLine(P, a) → b
  3. LineBisector(B, P) → c
  4. Intersect(b, c) → A
  5. Circle(A, B) → d
  6. Point(d) → Q
  7. Segment(P, Q) → e
  8. Angle(R, P, Q) → α
  9. Ray(P, Q) → f
  10. Mirror(R, P) → S
  11. Angle(Q, P, S) → β
  12. CircleArc(A, P, Q) → g
  13. CircleArc(A, Q, P) → h
  14. Point(h) → C
  15. Point(g) → D
  16. Segment(P, C) → i
  17. Segment(Q, C) → j
  18. Segment(P, D) → k
  19. Segment(Q, D) → l
  20. Angle(Q, C, P) → γ
  21. Angle(P, D, Q) → δ