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Chords Equidistant from Center

Chords Equidistant from Center
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2015-11-28 10:10
TriangleCircleGeometric Construction
In collections Circles (Theorems)
This example demonstrates the geometric properties of chords in a circle that are equidistant from the center. It involves core concepts like circles, chords, perpendicular diameters theorem, triangles, and angle measurement. The construction uses GeoGebra commands such as Circle, Point, Segment, Intersect, OrthogonalLine, and Angle. Suitable for high school mathematics teaching to explore chord properties and their relation to the perpendicular diameters theorem.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Segment(A, C) → a
  5. Segment(A, D) → b
  6. Intersect(e, a, 1) → E
  7. Intersect(e, b, 1) → F
  8. OrthogonalLine(E, a) → f
  9. OrthogonalLine(F, b) → g
  10. Segment(A, E) → h
  11. Segment(A, F) → i
  12. Intersect(c, f, 2) → G
  13. Intersect(c, f, 1) → H
  14. Intersect(c, g, 1) → I
  15. Intersect(c, g, 2) → J
  16. Segment(G, H) → j
  17. Segment(I, J) → k
  18. Angle(A, F, I) → α
  19. Angle(A, E, H) → β

AI Drawing Prompt Reference

Draw a circle and select two points A and B on it. Draw two chords AC and AD with A and B as endpoints. Construct perpendicular lines from points E and F to chords AC and AD, respectively. These perpendicular lines intersect the circle at points G, H, I, and J. Connect G and H, and I and J to form two chords equidistant from the center. Measure the angles ∠AFI and ∠AEH.
The prompt above was compiled from the original drawing commands and is for reference only.