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Angle in a Semi-circle

Angle in a Semi-circle
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2015-01-13 15:58
TriangleCircleAngleGeometric Construction
In collections Circle Theorems
This example demonstrates the geometric proof of the angle in a semi-circle theorem. It involves core math concepts like circles, triangles, angle measurement, and geometric properties. The construction uses GeoGebra commands such as Intersect, Circle, Point, Segment, OrthogonalLine, and Angle. Suitable for high school mathematics education and geometric theorem exploration, helping students visually understand geometric properties.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → O
  2. Circle(O, 4) → c
  3. Point(c) → A
  4. Point(c) → B
  5. Segment(A, B) → e
  6. OrthogonalLine(B, e) → f
  7. Intersect(c, f, 2) → C
  8. Segment(A, C) → g
  9. Segment(C, B) → h
  10. Angle(A, B, C) → α
  11. Angle(C, B, A) → β

AI Drawing Prompt Reference

Draw a triangle inside a semicircle. The center of the semicircle is O, with a radius of 4. Points A and B lie on the circle, connected by the semicircle arc. Draw a perpendicular line from point B to the chord AB, intersecting the circle at point C. Connect points A and C, and points C and B to form two triangles. Measure angles A, B, and C, and angles C, B, and A. Show these angle relationships to help understand the theorem of angles in a semicircle.
The prompt above was compiled from the original drawing commands and is for reference only.