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Inscribed Polygons Exercise: Semicircle Theorem

Inscribed Polygons Exercise: Semicircle Theorem
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2015-01-18 01:38
CirclePolygonAngleTransformationGeometric Construction
In collections MATHEMATICS and Geometry 9 : 8.3 Iscribed Polygons
This example demonstrates the properties of inscribed polygons, particularly the semicircle theorem. Key mathematical concepts include polygons, circles, and angles. Using GeoGebra commands such as constructing circles, rotating, and measuring angles, dynamic exploration of these geometric shapes is possible. Suitable for middle or high school geometry education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 10) → circle
  3. Intersect(circle, xAxis, 1) → A
  4. Intersect(circle, xAxis, 2) → B
  5. Segment(A, B) → a
  6. Rotate(A, 240*°, O) → C
  7. Angle(C, O, A) → α
  8. Segment(O, C) → b
  9. Segment(B, C) → c
  10. Segment(C, A) → d
  11. Angle(A, C, O) → β
  12. Angle(O, C, B) → γ
  13. Polygon(A, O, C) → polígono1, c_1, a_1, o
  14. Angle(B, A, C) → δ
  15. Angle(A, C, B) → Θ
  16. Angle(A, C, O) → ε
  17. Angle(O, C, B) → ζ