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Properties of Cyclic Quadrilaterals

Properties of Cyclic Quadrilaterals
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2019-06-29 05:33
CirclePolygonAngleTransformationGeometric Construction
This GeoGebra applet demonstrates a direct corollary of the inscribed angle theorem: in any cyclic quadrilateral, opposite angles are supplementary. The applet involves concepts of circles, angles, and polygons. Using GeoGebra commands such as Circle, Point, Rotate, CircleArc, Segment, Intersect, CircleSector, Dilate, Vector, Translate, Angle, Ray, and Polygon, students can visually understand the properties of cyclic quadrilaterals. Suitable for students in middle school and above for geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Rotate(C, 2°, A) → C'
  4. CircleArc(A, C', C) → d
  5. Point(d) → D
  6. CircleArc(A, D, C) → e
  7. Point(e) → E
  8. CircleArc(A, E, C) → f
  9. Point(f) → F
  10. CircleArc(A, F, C) → g
  11. Point(g) → G
  12. Segment(D, E) → b
  13. Segment(E, F) → h
  14. Segment(D, G) → a
  15. Segment(G, F) → i
  16. Circle(F, (0.2 * Distance[A, B])) → k
  17. Circle(E, (0.2 * Distance[A, B])) → p
  18. Circle(G, (0.2 * Distance[A, B])) → q
  19. Circle(D, (0.2 * Distance[A, B])) → r
  20. Intersect(k, i, 1) → H
  21. Intersect(k, h, 1) → I
  22. Intersect(p, h, 1) → J
  23. Intersect(p, b, 1) → K
  24. Intersect(r, a, 1) → L
  25. Intersect(r, b, 1) → M
  26. Intersect(q, a, 1) → N
  27. Intersect(q, i, 1) → O
  28. CircleSector(G, N, O) → s
  29. CircleSector(F, H, I) → t
  30. CircleSector(E, J, K) → c_1
  31. CircleSector(D, M, L) → d_1
  32. Circle(A, B) → e_1
  33. Dilate(E, If[0 < j ≤ 1, 1 - j, 0], G) → E'
  34. Vector(E, E') → u
  35. Translate(c_1, u) → f_1
  36. CircleArc(E, J, K) → g_1
  37. Translate(J, u) → J'
  38. Angle(O, G, J') → α
  39. Rotate(f_1, If[1 < j ≤ 2, ((-(j - 1)) * α), (-α)], G) → h_1
  40. Ray(D, G) → l
  41. Point(l) → P
  42. Ray(G, P) → m
  43. Dilate(F, If[2 < j ≤ 3, 3 - j, 0], D) → F'
  44. Vector(F, F') → v
  45. Ray(G, D) → n
  46. Point(n) → Q
  47. Ray(D, Q) → a_1
  48. Translate(t, v) → t'
  49. CircleArc(F, H, I) → k_1
  50. Translate(I, v) → I'
  51. Angle(I', D, M) → β
  52. Rotate(t', If[3 < j ≤ 4, ((j - 3) * β), β], D) → t''
  53. Polygon(G, D, E, F) → poly1, g_2, d_2, e_2, f_2