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Locus of Intersection of Tangents

Locus of Intersection of Tangents
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2016-04-19 22:09
CircleCoordinate GeometryDerivativeGeometric ConstructionLocus
This example demonstrates the locus of intersection points of tangents from a circle. Key math concepts include circle, tangent, differential calculus, coordinate geometry, and locus. It is constructed using GeoGebra commands like Circle, Point, Line, Intersect, Tangent, and Locus. Suitable for high school students and above to explore trajectory problems and calculus applications.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(C, B) → d
  3. Point(d) → D
  4. Line(B, D) → a
  5. Intersect(c, a, 2) → E
  6. Tangent(E, c) → b,
  7. Tangent(D, d) → e,
  8. Intersect(b, e) → F
  9. Locus(F, D) → loc1

AI Drawing Prompt Reference

Draw two circles that intersect at a point. From a point on the first circle, draw a tangent to the second circle. Then, from the intersection point of the second circle, draw a tangent to the first circle. The intersection of these two tangents traces a locus. Finally, plot this locus to show the path of the intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.