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Cyclic Quadrilateral by dsyddall

Cyclic Quadrilateral by dsyddall
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2012-06-27 02:34
CirclePolygonAngleTrigonometryGeometric Construction
This example demonstrates the geometric properties of a cyclic quadrilateral, focusing on its angle relationships. Core mathematical concepts involved include circles, quadrilaterals, angles, secant lines, and trigonometric functions such as cosine. Construction uses GeoGebra commands like Intersect to find intersections, Circle to draw circles, Point to create points, Polygon to construct polygons, Segment to draw segments, Angle to measure angles, and Vector to add vectors. Objects include the center O, circle c, points A, B, C, etc., for building the figure. Suitable for high school mathematics, particularly in geometry and trigonometry, for teaching or self-study.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 1) → c
  3. Point(c) → A
  4. Point(c) → C
  5. Point(c) → B
  6. Polygon(A, C, B) → poly1, e, c_1, d
  7. Segment(C, O) → b_1
  8. Segment(O, B) → g
  9. Angle(O, A, B) → b
  10. Angle(A, B, O) → b_2
  11. Angle(C, A, B) → circ
  12. Angle(C, O, B) → smallcentre
  13. Angle(C, O, B) → bigcentre
  14. Point(c) → F
  15. Angle(F, O, C) → cangle
  16. Angle(F, O, B) → bangle
  17. Angle(F, O, A) → aangle
  18. Angle(C, B, O) → isosceles1
  19. Vector(A, O) → u
  20. Vector(B, O) → v
  21. Vector(C, O) → w
  22. Angle(B, C, O) → isosceles2
  23. Angle(B, C, A) → isoscelespluscirc
  24. Angle(A, C, O) → α
  25. Angle(A, B, C) → β
  26. Point(c) → E
  27. Polygon(B, E, C) → poly2, c_2, b_3, e_1
  28. Angle(F, O, E) → eangle
  29. Angle(B, E, C) → δ
  30. Polygon(A, B, E, C) → poly3, a, b_4, e_2, c_3
  31. Angle(B, A, C) → γ
  32. Angle(B, E, C) → ε
  33. Angle(E, B, A) → ζ
  34. Angle(E, C, A) → η
  35. Vector(E, O) → z