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Secant Line Through External Point with Chord Endpoints as Midpoints

Secant Line Through External Point with Chord Endpoints as Midpoints
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2017-11-28 15:00
CircleCoordinate GeometryGeometric Construction
In collections M 333L F17 Constructions
This example demonstrates a secant line passing through an external point such that the endpoints of the chord are midpoints. Key mathematical concepts include the properties of circles and the midpoint theorem. The construction uses commands such as Circle, Segment, LineBisector, Intersect, and Point in GeoGebra. Suitable for middle school and above students to learn about circle properties and geometric construction.

GeoGebra Commands & Parameters

  1. Circle(O, C) → c
  2. Segment(A, O) → f
  3. LineBisector(f) → g
  4. Intersect(g, f) → B
  5. Circle(B, O) → d
  6. Intersect(c, d, 2) → D
  7. Segment(D, A) → h
  8. Circle(E, h) → e
  9. Point(e) → F
  10. Segment(E, F) → i
  11. LineBisector(i) → j
  12. Intersect(j, i) → G
  13. Circle(G, Segment[F, G]) → k
  14. Intersect(k, j, 1) → H
  15. Segment(H, F) → l
  16. Segment(H, E) → m
  17. Circle(A, m) → p
  18. Intersect(c, p, 1) → I
  19. Line(A, I) → n
  20. Intersect(c, n, 2) → J