MathPlotAI Logo MathPlotAI

Perpendicular bisector of a chord passes through the center

Perpendicular bisector of a chord passes through the center
Loading the math board and drawing, please wait…
2014-09-08 14:37
CircleAngleGeometric Construction
In collections Symmetry Properties of Circles
This example demonstrates the geometric property that the perpendicular bisector of a chord in a circle always passes through the center. It involves core math concepts like circles, perpendicular bisectors, symmetry, and geometric proofs. The construction uses GeoGebra commands/objects: Circle, Point, Segment, OrthogonalLine, Intersect, Distance, and Angle. Suitable for high school students to understand circle symmetry and geometric proofs.

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(f, e) → g
  13. Distance(Y, O) → distanceYO
  14. Distance(X, O) → distanceXO
  15. Angle(O, Y, D) → α
  16. Angle(O, X, B) → β
  17. Segment(O, D) → h
  18. Segment(O, C) → i
  19. Distance(D, Y) → distanceDY
  20. Distance(Y, C) → distanceYC

AI Drawing Prompt Reference

Draw a circle and mark two points on it. Connect the center to these points to form two segments. Circle each point with the radius equal to the distance to the center, intersecting the original circle at four new points. Connect these points in pairs to form two chords. Draw the perpendicular bisectors of these chords, which should intersect at the circle's center. Verify that the perpendicular bisectors pass through the center and measure the distances and angles to demonstrate the circle's symmetry and geometric properties.
The prompt above was compiled from the original drawing commands and is for reference only.