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Equal Chords Are Equidistant from the Center

Equal Chords Are Equidistant from the Center
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2014-09-08 14:05
CircleCoordinate GeometryGeometric Construction
In collections Symmetry Properties of Circles
This example demonstrates the property of equal chords being equidistant from the center of a circle. Key concepts include the center, radius, and perpendicular lines. Using GeoGebra commands such as Circle, Point, Segment, OrthogonalLine, Intersect, Distance, etc., the example provides a clear and interactive illustration. Suitable for students at the junior high school level and above.

GeoGebra Commands & Parameters

  1. Circle(O, radius) → k
  2. Point(Circle[O, OX]) → X
  3. Segment(O, X) → a
  4. Point(Circle[O, OY]) → Y
  5. Segment(O, Y) → b
  6. OrthogonalLine(Y, b) → c
  7. OrthogonalLine(X, a) → d
  8. Intersect(k, d) → B, A
  9. Intersect(k, c) → D, C
  10. Segment(B, A) → e
  11. Segment(C, D) → f
  12. Distance(e, f) → g
  13. Distance(Y, O) → distanceYO
  14. Distance(X, O) → distanceXO
  15. Angle(O, Y, D) → α
  16. Angle(O, X, B) → β