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Angles in the Opposite Segments

Angles in the Opposite Segments
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2014-06-10 04:30
CircleAngleGeometric Construction
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This example demonstrates the theorem of angles in the opposite segments of a circle, where opposite angles in a cyclic quadrilateral are supplementary. Key concepts include circle angles and cyclic quadrilaterals. It uses GeoGebra commands such as Circle, Segment, and Angle. Suitable for middle school and above students to learn geometric construction and circle properties.

GeoGebra Commands & Parameters

  1. Circle(O, Radius) → c
  2. Point(c) → A'
  3. Point(c) → C
  4. Point(c) → B
  5. Segment(C, B) → BC_1
  6. Segment(B, A') → AB
  7. Segment(A, B) → A'B
  8. Point(c) → D
  9. Segment(C, D) → CD
  10. Segment(O, B) → OB
  11. Segment(D, A') → AD
  12. Segment(C, B) → BC
  13. Angle(D, A', B) → BAD
  14. Angle(B, C, D) → BCD
  15. Angle(C, D, A') → ADC
  16. Angle(A', B, C) → ABC
  17. Segment(D, A) → a
  18. Angle(C, D, A) → ADC1
  19. Angle(A, B, C) → ABC1
  20. Angle(D, A, B) → BAD1
  21. Segment(D, O) → OD
  22. Angle(D, A', B) → α
  23. Angle(D, O, B) → Twoα
  24. Angle(B, O, D) → ReflectBOD
  25. Angle(B, C, D) → β

AI Drawing Prompt Reference

Draw a circle and mark points A', C, and B on it. Connect AC and BC. Take another point D on the circle and connect CD and BD. Label the angles BAD, BCD, ADC, and ABC. Connect A'B and A'D, and draw line OD to the center O. Label angles α, two α, and β to demonstrate the property that opposite angles in a cyclic quadrilateral are supplementary.
The prompt above was compiled from the original drawing commands and is for reference only.