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Angles Inside, Outside, and On Circle

Angles Inside, Outside, and On Circle
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2020-05-06 01:57
CircleAngleGeometric Construction
This example demonstrates the geometric relationships and properties of angles inside, outside, and on a circle, including the Inscribed Angle Theorem, Central Angle Theorem, and exterior angle theorem. It involves core mathematical concepts like trigonometric functions. The construction uses GeoGebra commands and objects such as Circle, Point, Line, Intersect, Angle, IsInRegion, Segment, LineBisector, and CircleArc. Suitable for high school geometry learning and math competition training, helping deepen the understanding of circle-angle relationships.

GeoGebra Commands & Parameters

  1. Circle(Center, radius) → c
  2. Point(c) → D
  3. Line(C, D) → a
  4. Point(c) → E
  5. Line(C, E) → b
  6. Intersect(c, b, 2) → F
  7. Intersect(c, a, 2) → G
  8. Angle(E, C, D) → α
  9. Angle(F, C, G) → β
  10. IsInRegion(C, c) → inside
  11. Segment(D, E) → h
  12. LineBisector(h) → i
  13. Intersect(c, i) → L, M
  14. LineBisector(G, F) → j
  15. Intersect(c, j) → B, N
  16. LineBisector(F, G) → k
  17. Intersect(c, k) → O, P
  18. LineBisector(D, E) → l
  19. Intersect(c, l) → Q, R
  20. Angle(E, Center, D) → γ
  21. Angle(G, Center, F) → δ
  22. CircleArc(Center, E, D) → d
  23. CircleArc(Center, G, F) → e
  24. Angle(F, Center, G) → ε