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Inscribed Angle in Semicircle Always 90 Degrees

Inscribed Angle in Semicircle Always 90 Degrees
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2014-07-28 00:55
CircleAngleGeometric Construction
This example demonstrates the geometric theorem that an inscribed angle in a semicircle is always 90 degrees. Key mathematical concepts include circle, angle, and right angle. Using GeoGebra commands such as Circle, Point, Segment, Line, Intersect, etc., a semicircle is constructed, and it is shown that when the vertex of an angle lies on the circumference and the sides intersect the diameter, the angle is always a right angle. Suitable for students at the junior high school level and above to learn geometric construction and circle properties.

GeoGebra Commands & Parameters

  1. Circle(A, Radius) → circle
  2. Point(circle) → B
  3. Point(circle) → D
  4. Segment(D, B) → d
  5. Line(B, A) → diameterLine
  6. Intersect(circle, diameterLine, 2) → C
  7. Segment(B, C) → a
  8. CircleArc(A, B, C) → c
  9. Segment(D, C) → b
  10. Line(D, C) → angleAnchorLineCD
  11. Angle(B, D, C) → α

AI Drawing Prompt Reference

Draw a semicircle with endpoints D and B on the diameter, select point C on the circle, connect B to C and D to C, then form angle DBC to demonstrate it is a right angle, illustrating circle properties and geometric construction.
The prompt above was compiled from the original drawing commands and is for reference only.