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Peculiarities of a Circumcircle

Peculiarities of a Circumcircle
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2017-09-03 09:26
CircleTransformationGeometric Construction
This example demonstrates the fascinating properties of a circumcircle. It involves basic concepts of circles such as the center, radius, and diameter. Using GeoGebra commands like Rotate, Angle, Ray, Circle, Intersect, Distance, Segment, etc., dynamic exploration of various circle properties is possible. Suitable for middle and high school students to learn geometric construction and circle-related concepts.

GeoGebra Commands & Parameters

  1. Rotate(A_1, a, A) → A'
  2. Angle(A_1, A, A') → α
  3. Ray(A, A_1) → f
  4. Ray(A, A') → g
  5. Circle(A, 4) → c
  6. Intersect(c, f) → B,
  7. Distance(A, f) → distanceBf
  8. Distance(A, B) → distanceBC
  9. Circle(A, 5) → d
  10. Intersect(d, g) → C,
  11. Distance(A, C) → distanceBD
  12. Segment(A, C) → h
  13. Segment(A, B) → i
  14. Segment(C, B) → j
  15. Circle(A, B, C) → e
  16. Center(e) → O
  17. Angle(A, C, B) → β
  18. Angle(C, B, A) → γ