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Complete Quadrangle and Circle Constructions

Complete Quadrangle and Circle Constructions
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2018-04-17 11:19
CircleTransformationGeometric Construction
This example demonstrates the construction of three circles using midpoints and intersections of a complete quadrangle. It involves core geometric construction concepts such as lines, intersections, midpoints, and circle construction. GeoGebra commands used include Line, Intersect, Segment, Midpoint, Circle, etc. Suitable for middle school and above students to learn about geometric constructions and properties of circles.

GeoGebra Commands & Parameters

  1. Line(D, A) → f
  2. Line(A, C) → g
  3. Line(C, B) → h
  4. Line(B, A) → i
  5. Line(D, C) → j
  6. Line(D, B) → k
  7. Intersect(f, h) → I_{AD∧BC}
  8. Intersect(k, g) → I_{AC∧BD}
  9. Intersect(j, i) → I_{AB∧CD}
  10. Segment(A, B) → r
  11. Segment(A, I_{AC∧BD}) → n
  12. Segment(B, I_{AD∧BC}) → p
  13. Midpoint(A, D) → M_{AD}
  14. Midpoint(D, B) → M_{BD}
  15. Midpoint(C, D) → M_{CD}
  16. Midpoint(A, B) → M_{AB}
  17. Midpoint(A, C) → M_{AC}
  18. Midpoint(C, B) → M_{BC}
  19. Segment(D, B) → m
  20. Segment(B, I_{AC∧BD}) → s
  21. Segment(D, A) → l
  22. Segment(D, C) → q
  23. Segment(C, I_{AB∧CD}) → a
  24. Circle(I_{AD∧BC}, M_{AD}, M_{BC}) → c
  25. Circle(I_{AC∧BD}, M_{BD}, M_{AC}) → d
  26. Circle(I_{AB∧CD}, M_{AB}, M_{CD}) → e
  27. Segment(I_{AC∧BD}, C) → b
  28. Segment(C, I_{AD∧BC}) → f_1
  29. Segment(A, I_{AB∧CD}) → t
  30. Segment(A, I_{AD∧BC}) → h_1
  31. Conic(M_{BD}, M_{BC}, M_{AC}, M_{AD}, I_{AB∧CD}) → p9
  32. Intersect(d, c) → I_{dc}1, I_{dc}2, ,
  33. Line(I_{dc}1, I_{dc}2) → Rx_{dc}
  34. Intersect(e, c) → I_{ec}1, I_{ec}2, ,
  35. Line(I_{ec}1, I_{ec}2) → Rx_{ec}
  36. Intersect(e, d) → I_{ed}1, I_{ed}2, ,
  37. Line(I_{ed}2, I_{ed}1) → Rx_{ed}
  38. Intersect(Rx_{ed}, Rx_{dc}) → Rc