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Inscribed Angle Theorem

Inscribed Angle Theorem
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2019-09-04 11:47
CircleAngleGeometric Construction
This example demonstrates the relationship between an inscribed angle and a central angle intercepting the same arc. It involves the concepts of inscribed angles and central angles. Using commands such as Circle, Point, Segment, and Angle, it shows that an inscribed angle is half of the central angle intercepting the same arc. Suitable for students at the junior high school level and above for geometric construction.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a circle and select three points A, B, and C on the circle. Connect points A and C, C and B, A and the center O, and B and O to form two chords and two radii. Measure the angles ∠ACB and ∠AOB to observe if ∠ACB is half of ∠AOB.
The prompt above was compiled from the original drawing commands and is for reference only.