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Defining a Circle

Defining a Circle
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2013-05-20 10:34
CircleCoordinate GeometryGeometric Construction
In collections Exploring Conic Sections
This example uses an animation to help students learn about the equation of a circle. It demonstrates the geometric definition of a circle and its equation derivation. Key math concepts include circle definition, coordinate geometry, and equation representation. GeoGebra commands used are: Circle, Intersect, OrthogonalLine, Rotate, Angle, Segment. Suitable for high school mathematics teaching, particularly for introductory coordinate geometry and understanding geometric transformations.

GeoGebra Commands & Parameters

  1. Circle(C, r) → c
  2. Intersect(xAxis, yAxis) → A
  3. OrthogonalLine(C, yAxis) → a
  4. OrthogonalLine(C, a) → b
  5. Intersect(c, a, 1) → B
  6. Rotate(B, α, C) → B'
  7. Angle(B, C, B') → β
  8. OrthogonalLine(B', a) → d
  9. Segment(C, B') → e
  10. Intersect(a, d) → D
  11. Segment(B', D) → f
  12. Segment(D, C) → g
  13. Angle(B', D, C) → γ