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Circle's Inscribed Quadrilateral Opposite Angles

Circle's Inscribed Quadrilateral Opposite Angles
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2014-10-06 22:16
CircleAngleGeometric ConstructionSlider Animation
In collections Circles Properties and Angle Properties of Circles
This example demonstrates the theorem that opposite angles in a cyclic quadrilateral are supplementary. It involves core math concepts like circle, angles, and the inscribed angle theorem. Constructed using GeoGebra commands such as Circle, Point, Angle, and Segment. Suitable for high school geometry education or learning about circle properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, B) → c
  3. Point(c) → A
  4. Rotate(B, -α_1, A) → C_1
  5. Ray(A, C_1) → b
  6. Intersect(c, b) → G, C
  7. Point(c) → D
  8. Angle(B, D, C) → α
  9. Segment(B, D) → a
  10. Segment(A, B) → g
  11. Angle(C, A, B) → β
  12. Segment(D, C) → d
  13. Segment(A, C) → h

AI Drawing Prompt Reference

Draw a circle and select a point on it. Connect the point to the center of the circle, then draw a ray from the point. Let the ray intersect the circle at two points. Connect the center to these two points, and connect the two intersection points. Measure the angles between the center, one intersection point, and the other point on the circle, showing that their sum is 180 degrees to demonstrate the property of a cyclic quadrilateral that opposite angles are supplementary.
The prompt above was compiled from the original drawing commands and is for reference only.