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The Angle at the Center is Twice the Angle at the Circumference

The Angle at the Center is Twice the Angle at the Circumference
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2014-08-11 20:42
CircleAngleGeometric Construction
This example illustrates the theorem that the angle at the center is twice the angle at the circumference. Key mathematical concepts include central angles and inscribed angles. Using GeoGebra commands such as Circle, Point, Polygon, Angle, and Line, a geometric figure with central and inscribed angles is constructed. Suitable for middle school and above students to study geometry.

GeoGebra Commands & Parameters

  1. Circle(O, 4) → c
  2. Point(c) → B
  3. Point(c) → C
  4. Point(c) → D
  5. Polygon(O, B, C, D) → poly1, a, b, c_1, d
  6. Angle(B, C, D) → α
  7. Angle(B, O, D) → β
  8. Line(C, O) → e
  9. Polygon(F, G, H) → poly2, h, f, g
  10. Line(H, F) → i
  11. Point(i) → I
  12. Angle(F, G, H) → γ
  13. Angle(G, H, F) → δ
  14. Angle(G, F, I) → ε

AI Drawing Prompt Reference

Draw a circle with center O and radius 4, then place points B, C, and D on the circle and connect them to form a quadrilateral. Draw angles BDC and BOD, then draw a line from C to O. Draw triangle FGH, connect points F, G, and H, and draw angles FGH, GHF, and GFH.
The prompt above was compiled from the original drawing commands and is for reference only.