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New Pythagorean Theorem for Non-Similar Circles

New Pythagorean Theorem for Non-Similar Circles
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2019-08-03 01:39
CircleTransformationGeometric Construction
This example demonstrates a new Pythagorean theorem for non-similar circles. It involves key mathematical concepts such as geometric mean and geometric transformations. Using GeoGebra commands like Circle, Point, Line, Segment, Midpoint, Circumference, PointIn, Area, the construction of this interesting geometric phenomenon is achieved. Suitable for high school geometry learners and math enthusiasts.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → C
  3. Point(c) → B
  4. Line(C, B) → f
  5. Point(c) → D
  6. Segment(D, C) → g
  7. Segment(D, B) → h
  8. Midpoint(C, D) → E
  9. Midpoint(D, B) → F
  10. Circle(E, D) → d
  11. Circle(F, D) → e
  12. Point(d) → G
  13. Segment(G, C) → i
  14. Segment(G, D) → j
  15. Point(e) → H
  16. Segment(D, H) → k
  17. Segment(H, B) → l
  18. Midpoint(G, C) → I
  19. Midpoint(G, D) → J
  20. Midpoint(D, H) → K
  21. Midpoint(H, B) → L
  22. Circle(I, G) → p
  23. Circle(J, G) → q
  24. Circle(K, D) → r
  25. Circle(L, H) → s
  26. Circumference(p) → cep
  27. PointIn(p) → Pointp_1
  28. Circumference(q) → ceq
  29. PointIn(q) → Pointq_1
  30. Circumference(r) → cer
  31. PointIn(r) → Pointr_1
  32. Circumference(s) → ces
  33. PointIn(s) → Points_1
  34. Circumference(c) → downbig
  35. PointIn(c) → Pointc_1
  36. Circumference(c) → circumferencec
  37. PointIn(c) → Pointc_2
  38. Area(p) → b
  39. PointIn(p) → Pointp
  40. Area(q) → m
  41. PointIn(q) → Pointq
  42. Area(r) → n
  43. PointIn(r) → Pointr
  44. Area(s) → o
  45. PointIn(s) → Points
  46. Area(c) → t
  47. PointIn(c) → Pointc