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Properties of Perpendicular Lines to Chords of Circles

Properties of Perpendicular Lines to Chords of Circles
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2017-05-05 21:19
CircleAngleGeometric Construction
In collections Unit 9 - Circles
This applet demonstrates the geometric properties of perpendicular lines drawn to chords of circles. It covers core concepts like the perpendicular bisector theorem, central angles, and chord distances. Constructed using GeoGebra commands such as Circle, Point, Segment, Intersect, Angle, OrthogonalLine, and Distance. Ideal for high school students studying circle geometry and properties.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(B, C) → a
  4. Point(c) → D
  5. Circle(D, Segment[C, B]) → d
  6. Intersect(c, d, 1) → E
  7. Segment(A, B) → b
  8. Segment(A, C) → e
  9. Segment(A, D) → f
  10. Segment(A, E) → g
  11. Segment(D, E) → h
  12. Angle(B, A, C) → α
  13. Angle(D, A, E) → β
  14. OrthogonalLine(A, a) → i
  15. OrthogonalLine(A, h) → j
  16. Intersect(j, h) → F
  17. Intersect(i, a) → G
  18. Angle(A, G, B) → γ
  19. Angle(A, F, D) → δ
  20. Distance(C, G) → distanceCG
  21. Distance(G, B) → distanceGB
  22. Distance(D, F) → distanceDF
  23. Distance(E, F) → distanceEF
  24. Distance(A, G) → distanceAG
  25. Distance(A, F) → distanceAF

AI Drawing Prompt Reference

Draw a circle and a chord inside it. Then, draw a concentric circle with the midpoint of the chord as the center. Find the intersection points of the two circles. Connect the center to these points and draw perpendicular lines to the chord. Measure the chord's length, central angles, and the relationships between the perpendicular segments and the chord, labeling key distances.
The prompt above was compiled from the original drawing commands and is for reference only.