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Tangents from External Points are Equal

Tangents from External Points are Equal
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2014-09-08 15:45
CircleAngleGeometric Construction
In collections Symmetry Properties of Circles
This example dynamically illustrates the property that tangents drawn from an external point to a circle are equal in length. It involves core math concepts like circle tangents, congruent triangles (Pythagorean Theorem), and symmetry. GeoGebra commands used include Circle, Tangent, Intersect, Segment, and Angle to construct the illustration. Suitable for high school geometry teaching to help students visually understand and prove the tangent length theorem, enhancing spatial reasoning skills.

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(O, C, D) → α
  11. Angle(E, C, O) → β
  12. Angle(O, E, C) → γ
  13. Angle(C, D, O) → δ

AI Drawing Prompt Reference

Draw a circle with a point outside it. Draw two tangent lines from the point to the circle, marking the points where they touch. Connect the point to the circle center and the points of tangency. Also, connect the center to each point of tangency. Measure the angles between the tangent lines and the radii. Display these angles. The final illustration should show the tangents are equal, the radii are perpendicular to the tangents, and the triangles formed are congruent, proving the tangent length theorem.
The prompt above was compiled from the original drawing commands and is for reference only.