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Angle between tangents from external point

Angle between tangents from external point
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2014-09-08 16:38
CircleAngleVectorTrigonometryGeometric Construction
In collections Symmetry Properties of Circles
This example demonstrates the angle formed by two tangents drawn from an external point to a circle, intersecting the circle at two points. Key math concepts include circle, tangent, angle, similar triangles, reflection, and similarity transformation. It is constructed using GeoGebra commands like Circle, Tangent, Intersect, Segment, and Angle. Suitable for high school students learning geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Circle(O, B) → c
  2. Tangent(C, c) → a, b
  3. Intersect(c, b) → D
  4. Intersect(c, a) → E
  5. Segment(C, D) → d
  6. Segment(C, E) → e
  7. Segment(C, O) → f
  8. Segment(D, O) → g
  9. Segment(E, O) → h
  10. Angle(E, C, D) → α
  11. Angle(O, C, D) → β
  12. Angle(E, C, O) → γ

AI Drawing Prompt Reference

Draw a circle and two tangents from an external point, intersecting the circle at two points. Connect these points to the circle's center and the center to the points of tangency. Then measure the angle between the tangents, the angles formed by the tangents and the line segments from the center to the points of tangency.
The prompt above was compiled from the original drawing commands and is for reference only.