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Angle Between Tangent and Chord

Angle Between Tangent and Chord
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2013-10-10 07:49
CircleAngleGeometric Construction
This GeoGebra applet illustrates the theorem that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. Key mathematical concepts include circle, tangent, chord, and inscribed angle. The construction uses commands like Circle, Tangent, Segment, and Angle. Suitable for students in middle school and above studying geometry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Point(c) → D
  4. Tangent(D, c) → a,
  5. Segment(D, C) → b
  6. Point(c) → E
  7. Segment(D, E) → d
  8. Segment(E, C) → e
  9. Point(a) → F
  10. Segment(C, D) → f
  11. Angle(C, D, F) → α
  12. Angle(C, E, D) → β
  13. Ray(D, F) → g
  14. Point(g) → H
  15. Segment(H, D) → h
  16. CircumcircleSector(C, E, D) → k
  17. Polygon(C, A, D) → poly1, d_1, c_1, a_1

AI Drawing Prompt Reference

Draw a circle and select two points on it. Draw a tangent at one point and connect the two points to form a chord. Take another point on the circle and connect it to both ends of the chord. Measure the angle between the tangent and the chord, and the angle between the chord and the line connecting the new point to the other end of the chord; they are equal. Finally, draw a sector with the chord as one side and the angle formed by the tangent and the chord as the central angle to illustrate the relationship between the angle in the alternate segment and the inscribed angle.
The prompt above was compiled from the original drawing commands and is for reference only.