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Similar Circles?

Similar Circles?
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2016-07-10 11:32
CircleTransformationGeometric Construction
In collections Circles (Theorems) Similarity Theorems! Circle Terms
This dynamic illustration demonstrates that all circles are similar, involving concepts like similarity transformation and continuity. It uses commands such as Circle, Point, Segment, Dilate, Vector, Translate, and Intersect. Suitable for high school students to understand similarity principles and transformation applications.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Circle(C, D) → d
  3. Point(c) → E
  4. Point(d) → F
  5. Segment(A, E) → a
  6. Segment(C, F) → b
  7. Dilate(C, If[0 < a_1 ≤ 1, 1 - a_1, 0], A) → C'
  8. Vector(C, C') → u
  9. Translate(d, u) → d'
  10. Translate(C, u) → C'_1
  11. Translate(C, u) → C'_2
  12. Translate(F, u) → F'
  13. Segment(C'_2, F') → g'
  14. Intersect(h, a, 1) → G
  15. Dilate(G, If[2 < a_1 ≤ 3, 3 - a_1, 0], E) → G'
  16. Circle(A, G') → k