MathPlotAI Logo MathPlotAI

Angle at the Centre is Twice the Angle at the Circumference

Angle at the Centre is Twice the Angle at the Circumference
Loading the math board and drawing, please wait…
2013-04-09 06:27
CircleAngleGeometric Construction
This example illustrates that the angle at the center of a circle is twice the angle at the circumference subtended by the same arc or chord. Key mathematical concepts include central angles, inscribed angles, and chords. The construction uses commands such as Circle, Point, Segment, Angle, and CircleArc in GeoGebra. Suitable for middle school and above students to learn about circle geometry.

GeoGebra Commands & Parameters

  1. Circle(O, B_1) → c
  2. Point(c) → A
  3. Point(c) → B
  4. Point(c) → C
  5. Segment(A, O) → a
  6. Segment(O, B) → b
  7. Segment(A, C) → d
  8. Segment(C, B) → e
  9. Angle(A, C, B) → α
  10. Angle(A, O, B) → β
  11. CircleArc(O, A, B) → f
  12. Segment(A, B) → g

AI Drawing Prompt Reference

Draw a circle with center O, and mark three points A, B, and C on the circle. Connect OA, OB, AC, and BC. Measure angle ACB and angle AOB. Draw arc AB and connect AB. Observe that angle AOB is twice angle ACB.
The prompt above was compiled from the original drawing commands and is for reference only.