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Circumference Angles Example

Circumference Angles Example
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2023-03-13 03:37
CircleAngleGeometric Construction
In collections geometriadinamica.es
This example demonstrates the properties and proof process of the inscribed angle theorem in geometry; involves core math concepts like inscribed angles, central angles, and equal arcs; constructed using GeoGebra commands such as Circle, Point, CircumcircleArc, Segment, Angle, Rotate; suitable for high school mathematics teaching and geometric construction practice.

GeoGebra Commands & Parameters

  1. Circle(O, 4) → c
  2. Point(c) → A
  3. Point(c) → B_1
  4. Point(c) → B
  5. CircumcircleArc(A, B_1, B) → h
  6. Point(h) → P
  7. Segment(A, P) → a
  8. Segment(P, B) → b
  9. Point(h) → Q
  10. Angle(A, Q, B) → α
  11. Segment(A, Q) → d_1
  12. Segment(Q, B) → e
  13. Segment(B, O) → f
  14. Segment(O, A) → g
  15. Angle(A, P, B) → β
  16. Angle(A, O, B) → γ
  17. Angle(A, O, D) → δ
  18. Rotate(D, (-δ), O) → C
  19. Rotate(F, (-δ), O) → G
  20. Angle(C, E, G) → ε
  21. Segment(E, C) → i
  22. Segment(E, G) → j
  23. Angle(B, H, I) → ζ
  24. Rotate(I, ζ, H) → K
  25. Rotate(J, ζ, H) → L
  26. Segment(L, H) → k
  27. Segment(H, K) → l
  28. Angle(L, H, K) → η

AI Drawing Prompt Reference

Draw a circle with center O and radius 4, then select three points A, B1, and B on the circle. Connect A and B1, B1 and B, and B and A to form arc h. Select two points P and Q on arc h, connect A and P, P and B, A and Q, and Q and B, and measure angles AQB, APB, and AOB. Then rotate points D and F to form new points C and G, connect C and G, and measure angle CEG. Finally, rotate points I and J to form new points K and L, connect K and L, and measure angle KHL.
The prompt above was compiled from the original drawing commands and is for reference only.