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Angle Between Tangent and Radius

Angle Between Tangent and Radius
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2013-10-09 10:26
CircleAngleGeometric Construction
This applet illustrates the theorem that the angle between a tangent and a radius at the point of contact is a right angle. Key mathematical concepts include circles, tangents, and angles. Using GeoGebra commands such as Circle, Tangent, Ray, and Angle, this example provides a visual demonstration of this geometric property. Suitable for students in middle school and above studying geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Circle(O, B) → c_1
  2. Point(c_1) → D
  3. Tangent(D, c_1) → a,
  4. Point(a) → F
  5. Ray(D, F) → g
  6. Point(g) → H
  7. Segment(O, D) → d
  8. Segment(X, H) → e
  9. Dilate(X, c, H) → C
  10. Line(C, D) → b
  11. Intersect(c_1, b, 2) → A
  12. Segment(A, D) → f
  13. Angle(O, D, A) → α
  14. Angle(O, D, C) → β
  15. Segment(C, D) → h

AI Drawing Prompt Reference

Draw a circle O, then take a point D on the circle, construct the tangent a at point D, draw a ray g from D intersecting tangent a at point F, then draw line segment OD, extend OC to point H, draw line segment CD, and finally draw line segment AD. Measure the angles ∠ODA and ∠ODC.
The prompt above was compiled from the original drawing commands and is for reference only.