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Secants and Tangents Product

Secants and Tangents Product
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2013-03-02 00:01
CircleTrigonometryGeometric Construction
In collections Unit 9 - Circles
This example demonstrates the relationship between secant and tangent segment products. Key mathematical concepts include circle properties and the secant theorem. It is constructed using GeoGebra commands such as Circle, Point, Ray, Segment, etc. Suitable for students from junior high school and above to learn geometry and algebra.

GeoGebra Commands & Parameters

  1. Circle(O, r) → c
  2. Point(c) → A
  3. Point(c) → B_1
  4. Point(c) → D
  5. Point(c) → B
  6. Ray(A, B) → a
  7. Ray(B_1, D) → b
  8. Point(c) → C
  9. Segment(O, C) → d
  10. OrthogonalLine(C, d) → e
  11. Line(A, B) → f
  12. Intersect(e, f) → P
  13. Segment(A, B) → ab
  14. Segment(B, P) → bp
  15. Segment(C, P) → cp
  16. Segment(A, P) → ap

AI Drawing Prompt Reference

Draw a circle and select four points A, B₁, D, and B on it. Draw a ray from A to B, and another ray from B₁ to D. Choose point C on the circle and draw a segment from the center O to C. Then draw a line through C that is perpendicular to OC. This line intersects the extension of AB at point P. Finally, draw segments AB, BP, CP, and AP to explore their relationships.
The prompt above was compiled from the original drawing commands and is for reference only.