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Inscribed Polygons Exercise: Semicircle Theorem by Jose Arturo Gomez Velasquez

Inscribed Polygons Exercise: Semicircle Theorem by Jose Arturo Gomez Velasquez
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2015-01-18 09:24
CirclePolygonAngleGeometric Construction
In collections MATHEMATICS and Geometry 9 : 8.3 Iscribed Polygons
This example demonstrates the properties of inscribed polygons, particularly the semicircle theorem. Key concepts include circles, polygons, and angles. Using GeoGebra commands such as Intersect, Circle, Point, Segment, Angle, and Rotate, it shows how to construct geometric figures. Suitable for junior high school geometry.

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. Point(Circle[O, 10]) → C
  6. Segment(A, C) → b_2
  7. Segment(O, A) → c
  8. Segment(O, B) → d
  9. Segment(B, C) → e
  10. Angle(C, B, O) → α
  11. Angle(O, A, C) → β_1
  12. Angle(C, B, O) → λ
  13. Angle(A, C, B) → γ
  14. Angle(A, C, B) → δ
  15. Angle(O, A, C) → β
  16. Angle(C, B, O) → ε
  17. Angle(O, A, C) → ζ
  18. Rotate(O, 70*°, A) → O'
  19. Ray(A, O') → a
  20. Intersect(circle, a, 2) → D
  21. Polygon(A, B, C) → polígono1, c_1, a_1, b
  22. Vector(E, C) → u

AI Drawing Prompt Reference

Draw a circle and inscribe a triangle inside it, connecting the center of the circle to the vertices of the triangle. Take a point on the circle and connect it to two vertices of the triangle. Measure the interior angles of the triangle and the central angles. Rotate the center slightly and draw a ray that intersects the circle at another point. Connect this new intersection point to the point on the circle, forming a quadrilateral. Measure all angles and label key points and segments.
The prompt above was compiled from the original drawing commands and is for reference only.