MathPlotAI Logo MathPlotAI

8.3 Inscribed Polygons: Semicircle Theorem Exercise 1.h

8.3 Inscribed Polygons: Semicircle Theorem Exercise 1.h
Loading the math board and drawing, please wait…
2015-01-19 22:37
CirclePolygonAngleGeometric Construction
In collections MATHEMATICS and Geometry 9 : 8.3 Iscribed Polygons
This example demonstrates the geometric properties of inscribed polygons within a semicircle. Key math concepts include the Inscribed Angle Theorem and properties of inscribed quadrilaterals. Construction highlights the use of GeoGebra commands such as Intersect, Circle, Point, Polar, OrthogonalLine, Rotate, Angle, Ray, Polygon, Segment, and CircumcircleArc, involving objects like texto1_1, O, texto2, circle, texto7_1, A, a, b, B, A', α, c, C, polígono1, c_1, a_1, b_1, D, D', e, E, polígono2, e_1, d, o, f, g, β, texto1_2, texto5_1, texto3_1, texto5_2, texto6_1, ϕ, texto1_3, γ, δ, ε, F, G. Suitable for high school students learning geometric constructions and theorem applications.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 10) → circle
  3. Point(circle) → A
  4. Polar(A, circle) → a
  5. OrthogonalLine(A, a) → b
  6. Intersect(circle, b, 2) → B
  7. Rotate(A, 28*°, B) → A'
  8. Angle(A, B, A') → α
  9. Ray(B, A') → c
  10. Intersect(circle, c, 2) → C
  11. Polygon(A, B, C) → polígono1, c_1, a_1, b_1
  12. Point(circle) → D
  13. Rotate(D, 332*°, B) → D'
  14. Ray(B, D') → e
  15. Intersect(circle, e, 2) → E
  16. Polygon(D, O, E) → polígono2, e_1, d, o
  17. Segment(D, E) → f
  18. Segment(C, A) → g
  19. Angle(D, E, O) → β
  20. Angle(B, C, A) → ϕ
  21. Angle(polígono2) → γ, δ, ε
  22. Point(circle) → F
  23. Point(circle) → G
  24. CircumcircleArc(C, F, A) → h
  25. CircumcircleArc(D, G, E) → k
  26. Polygon(D, O, E) → polígono3, e_2, d_1, o_1
  27. Polygon(A, B, C) → polígono4, c_2, a_2, b_2