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Tangent to Parabola and Circumcircle

Tangent to Parabola and Circumcircle
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2015-10-22 00:41
CircleFunctionGeometric Construction
This example demonstrates the relationship between the tangent to a parabola and its circumcircle. Key mathematical concepts include the properties of parabolas, tangents, and circles. Using GeoGebra commands such as Line, Parabola, Tangent, Intersect, and Circle, one can visually understand the interactions between these geometric elements. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Parabola(F, a) → c
  3. Point(c) → D
  4. Point(c) → E
  5. Point(c) → C
  6. Tangent(D, c) → b,
  7. Tangent(E, c) → d,
  8. Tangent(C, c) → e,
  9. Intersect(b, e) → G
  10. Intersect(d, e) → H
  11. Intersect(b, d) → I
  12. Circle(I, G, H) → f
  13. Prove(AreConcyclic[I, G, H, F]) → g