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Angle Subtended at Centre and Circumference

Angle Subtended at Centre and Circumference
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2019-07-10 06:39
CircleAngleGeometric Construction
This example demonstrates that the angle subtended at the center of a circle is twice the angle subtended at the circumference. Key mathematical concepts include the relationship between central and inscribed angles. It uses commands like Point, Segment, Angle, and CircleArc in GeoGebra. Suitable for middle school and above students for geometric construction.

GeoGebra Commands & Parameters

  1. Point(c) → A
  2. Point(c) → B
  3. Point(c) → D
  4. Segment(A, D) → a
  5. Segment(D, B) → b
  6. Segment(B, O) → d
  7. Segment(O, A) → e
  8. Angle(A, D, B) → α
  9. Angle(A, O, B) → γ
  10. CircleArc(O, A, B) → f

AI Drawing Prompt Reference

Draw a circle and select two points on its circumference. Connect each point to the center of the circle to form two line segments. Then, connect the two points to form an arc. Measure the central angle and the inscribed angle, demonstrating that the central angle is twice the inscribed angle to verify their relationship.
The prompt above was compiled from the original drawing commands and is for reference only.