MathPlotAI Logo MathPlotAI

Diameters and Chords Relationship in a Circle

Diameters and Chords Relationship in a Circle
Loading the math board and drawing, please wait…
2016-05-04 20:55
CircleCoordinate GeometryGeometric Construction
In collections Circles (Theorems)
This applet engages students to discover that in a circle, if a diameter is perpendicular to a chord, it bisects the chord. Key mathematical concepts include circle properties and perpendicular line segments. GeoGebra commands used include Circle, Intersect, CircleArc, Point, Segment, OrthogonalLine, Dilate, Rotate, Angle. Suitable for middle school and above students for geometric construction.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Intersect(c, a, 1) → C
  3. Intersect(c, a, 2) → D
  4. CircleArc(A, C, D) → d
  5. Point(d) → E
  6. CircleArc(A, E, D) → e
  7. Point(e) → F
  8. Segment(E, F) → f
  9. OrthogonalLine(A, f) → g
  10. Intersect(g, f) → G
  11. Circle(G, (0.2 * Distance[A, B])) → h
  12. Intersect(h, g, 2) → H
  13. Intersect(h, g, 1) → I
  14. Intersect(h, f, 1) → J
  15. Intersect(h, f, 2) → K
  16. Intersect(c, g, 1) → L
  17. Intersect(c, g, 2) → M
  18. Dilate(E, If[0 < b ≤ 1, 1 - b, 0], F) → E'
  19. Segment(E, E') → i
  20. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], L) → A'
  21. Dilate(A, If[1 < b ≤ 2, 2 - b, 0], M) → A'_1
  22. Segment(A, A'_1) → j
  23. Segment(A, A') → k
  24. CircleArc(A, L, F) → q
  25. CircleArc(A, E, L) → r
  26. Segment(G, F) → l
  27. Segment(E, G) → m
  28. Rotate(G, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 2), 1.5707963267948966], G) → G'_1
  29. Rotate(F, If[3.5 < b ≤ 4.5, ((b - 3.5) * π / 2), 1.5707963267948966], G) → F'_1
  30. Rotate(G, If[2.5 < b ≤ 3.5, ((b - 2.5) * π), 3.141592653589793], G) → G'_2
  31. Rotate(F, If[2.5 < b ≤ 3.5, ((b - 2.5) * π), 3.141592653589793], G) → F'_2
  32. Segment(G'_2, F'_2) → l'
  33. Rotate(F, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * π / 2), -1.5707963267948966], A) → F'_3
  34. CircleArc(A, F'_3, F) → t
  35. Angle(L, A, F) → α
  36. Rotate(L, If[4.5 < b ≤ 5.5, ((-(b - 4.5)) * α), (-α)], A) → L'
  37. CircleArc(A, E, L') → c_1
  38. Angle(F, G, A) → β
  39. Rotate(q, If[3.5 < b ≤ 4.5, ((-(b - 3.5)) * α), (-α)], A) → q'