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External Tangents to a Circle

External Tangents to a Circle
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2016-06-26 19:55
CircleCoordinate GeometryGeometric Construction
In collections Circles Properties and Angle Properties of Circles
This example demonstrates how to construct external tangents to a circle and explore their geometric properties. It involves core math concepts like circles, tangents, angles, intersecting lines, and coordinate geometry. The construction uses GeoGebra commands and objects such as If, Circle, Point, Segment, Tangent, Intersect, Angle, rectangle2endpointsthin, rectanglefrom2endpoints, Polygon, IsInRegion, Element, and more. Suitable for high school students learning geometric constructions, circle properties, and analytical geometry.

GeoGebra Commands & Parameters

  1. If(SelectedIndex[listAnsQ3] ≟ 4, true, false) → Qn3correct
  2. If(SelectedIndex[listAnsQ1] ≟ 5, true, false) → Qn1correct
  3. If(SelectedIndex[listAnsQ5] ≟ 5, true, false) → Qn5correct
  4. If(SelectedIndex[listAnsQ2] ≟ 3, true, false) → Qn2correct
  5. If(SelectedIndex[listAnsQ4] ≟ 5, true, false) → Qn4correct
  6. Circle(O, R) → c
  7. Point(c) → F
  8. Segment(O, F) → e
  9. Tangent(F, c) → b,
  10. Point(b) → D
  11. Point(b) → C
  12. Segment(C, D) → g
  13. Point(c) → E
  14. Tangent(E, c) → a,
  15. Point(a) → B
  16. Point(a) → A
  17. Segment(A, B) → h
  18. Intersect(g, h) → S
  19. Segment(O, S) → f
  20. Circle(O, (0.13 * Distance[O, S])) → c_1
  21. Intersect(c_1, e) → I,
  22. Intersect(c_1, f) → H,
  23. Segment(O, E) → d
  24. Intersect(c_1, d) → G,
  25. Segment(E, S) → m
  26. Circle(S, (0.25 * Distance[O, S])) → p
  27. Intersect(p, m) → L,
  28. Intersect(p, f) → J,
  29. Segment(F, S) → n
  30. Intersect(p, n) → K,
  31. Angle(O, E, B) → α
  32. Angle(O, F, D) → β
  33. rectangle2endpointsthin(E, L) → poly1
  34. rectangle2endpointsthin(F, K) → poly2
  35. rectangle2endpointsthin(O, J) → poly3
  36. rectanglefrom2endpoints(O, E) → poly4
  37. rectanglefrom2endpoints(O, F) → poly5
  38. Polygon(G, H, O) → poly6, t, a_1, b_1
  39. Polygon(H, I, O) → poly7, i, d_1, e_1
  40. Polygon(J, K, S) → poly8, j, k, q
  41. Polygon(J, L, S) → poly9, l, r, s
  42. IsInRegion(K_p, poly5) → touchOF
  43. IsInRegion(K_p, poly4) → touchOE
  44. Element(listFeedbackQ5, SelectedIndex[listAnsQ5]) → txtQ5F
  45. Element(listFeedbackQ2, SelectedIndex[listAnsQ2]) → txtQ2F
  46. Segment(O, S) → f_d
  47. Angle(S, O, E) → γ
  48. Segment(O, F) → e_d
  49. Segment(O, E) → d_d
  50. Angle(F, O, S) → δ
  51. Angle(O, S, F) → ε
  52. Angle(E, S, O) → ζ
  53. rectangle2endpointsthin1(C, D) → poly10LineCD
  54. rectangle2endpointsthin1(A, B) → poly11LineAB
  55. IsInRegion(K_p, poly10LineCD) → touchCD
  56. IsInRegion(K_p, poly11LineAB) → touchAB