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Common Tangents to a Circle (Proof)

Common Tangents to a Circle (Proof)
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2013-06-27 19:32
CircleAngleTrigonometryGeometric Construction
This example demonstrates how to construct and prove common tangents to a circle using GeoGebra. It involves core mathematical concepts such as circles, tangent lines, angles, and trigonometry. Key GeoGebra commands and objects used include Circle, Midpoint, Intersect, Ray, Segment, and Angle. Suitable for high school students learning geometric proofs and constructions.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Midpoint(A, C) → D
  3. Circle(D, C) → d
  4. Intersect(c, d) → E, F, ,
  5. Ray(C, E) → a
  6. Ray(C, F) → b
  7. Segment(E, C) → e
  8. Segment(C, F) → f
  9. Segment(A, C) → g
  10. Segment(E, A) → h
  11. Segment(A, F) → i
  12. Angle(A, E, C) → α
  13. Angle(C, F, A) → β

AI Drawing Prompt Reference

Draw a circle and another circle with its center at the midpoint of the diameter of the first circle. Find the intersection points of the two circles. Draw rays from the center of the first circle to these intersection points. Connect each intersection point to the center of the first circle and the other intersection point. Label the angles formed by the center of the first circle and the intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.