MathPlotAI Logo MathPlotAI

Angle Between Line AB and Circle Radius by Lew W. S.

Angle Between Line AB and Circle Radius by Lew W. S.
Loading the math board and drawing, please wait…
2016-05-27 04:16
CircleAngleTrigonometryGeometric Construction
This example demonstrates how to determine the angle between a tangent to a circle and its radius. It involves core mathematical concepts such as circles, tangents, angle measurement, and geometric construction. Key GeoGebra commands used include Circle, Line, Intersect, OrthogonalLine, Tangent, Angle, Segment, If, Point, and Distance. Suitable for high school mathematics education, this resource facilitates exploratory learning to help students understand the relationship between tangents and radii.

GeoGebra Commands & Parameters

  1. Circle(O, circle__radius) → c
  2. Line(A, B) → f
  3. Intersect(c, f) → C, D
  4. OrthogonalLine(O, f) → g
  5. Intersect(c, g) → E, F
  6. Intersect(f, g) → G
  7. Tangent(E, c) → h,
  8. OrthogonalLine(B, f) → i
  9. OrthogonalLine(A, f) → j
  10. Intersect(i, h) → H
  11. Intersect(h, j) → I
  12. Angle(H, E, O) → α
  13. Segment(O, D) → k
  14. Segment(O, C) → l
  15. Segment(A, B) → m
  16. Segment(E, G) → d_e
  17. Segment(O, E) → n
  18. Segment(I, E) → p
  19. Segment(E, H) → q
  20. Angle(O, D, C) → β
  21. Angle(D, C, O) → γ
  22. Segment(F, G) → d_f
  23. Segment(O, F) → r
  24. Tangent(F, c) → s,
  25. Intersect(s, j) → J
  26. Intersect(i, s) → K
  27. Angle(J, F, O) → δ
  28. If(SelectedIndex[listAnsQ1] ≟ 6, true, false) → Qn1correct
  29. If(SelectedIndex[listAnsQ2] ≟ 2, true, false) → Qn2correct
  30. If(SelectedIndex[listAnsQ3] ≟ 3, true, false) → Qn3correct
  31. If(SelectedIndex[listAnsQ4] ≟ 5, true, false) → Qn4correct
  32. Circle(Q_o, Q_t) → d
  33. Segment(Q_o, Q_t) → radius_4
  34. Point(d) → Q_c
  35. Segment(Q_t, Q_c) → chord_4
  36. Tangent(Q_t, d) → l_{q4},
  37. Point(l_{q4}) → Q_a
  38. Point(l_{q4}) → Q_b
  39. Segment(Q_a, Q_b) → tangent_4
  40. OrthogonalLine(Q_t, tangent_4) → t
  41. Intersect(d, t, 2) → Q_d
  42. Segment(Q_t, Q_d) → diameter_4
  43. Distance(I, F) → IF