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New Theorem of Pythagoras Circle

New Theorem of Pythagoras Circle
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2019-07-30 01:57
TriangleCircleGeometric Construction
This example demonstrates a new theorem within the Pythagorean circle, showcasing its geometric properties. Core math concepts include the Pythagorean theorem, circles, area, and geometric transformations. It utilizes commands and objects like Circle, Point, Line, Intersect, Segment, Rotate, Angle, Midpoint, Area, PointIn, Circumference, OrthogonalLine from GeoGebra for construction. Suitable for high school mathematics students and geometry enthusiasts.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Point(c) → C
  3. Line(C, A) → f
  4. Intersect(c, f, 2) → D
  5. Point(c) → B
  6. Segment(B, C) → g
  7. Point(f) → E
  8. Rotate(E, 90°, C) → E'
  9. Point(f) → F
  10. Segment(B, D) → h
  11. Angle(D, B, C) → α
  12. Midpoint(D, B) → G
  13. Midpoint(B, C) → H
  14. Circle(G, B) → d
  15. Circle(H, C) → e
  16. Area(d) → b
  17. PointIn(d) → Pointd_1
  18. Area(e) → i
  19. PointIn(e) → Pointe_1
  20. Area(c) → j
  21. PointIn(c) → Pointc_1
  22. Circumference(d) → circumferenced
  23. PointIn(d) → Pointd
  24. Circumference(e) → circumferencee
  25. PointIn(e) → Pointe
  26. Circumference(c) → circumferencec
  27. PointIn(c) → Pointc
  28. Intersect(d, e, 2) → I
  29. OrthogonalLine(B, f) → k
  30. Angle(B, I, D) → β