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Circle Theorem 2 – Angles in a Semicircle

Circle Theorem 2 – Angles in a Semicircle
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2012-07-14 21:38
CircleAngleGeometric Construction
① This example demonstrates that any angle inscribed in a semicircle is a right angle. ② Core mathematical concepts: the inscribed angle theorem, semicircle, right angle, and properties of circles. ③ Construction highlights: GeoGebra commands Circle (to create the circle), Point (to place endpoints and a movable point), Ray, Intersect, Segment (to build rays, intersection points, and segments), and Angle (to measure the angle); objects include circle c, points A, B, C, D, segments a, b, d, and angle α. ④ Suitable for middle‑school geometry (grade 9) and high‑school review, as well as teacher demonstrations and student‑led exploration.

GeoGebra Commands & Parameters

  1. Circle(A, 5) → c
  2. Point(c) → B
  3. Ray(B, A) → b
  4. Intersect(c, b, 2) → C
  5. Point(c) → D
  6. Segment(B, D) → a
  7. Segment(D, C) → d
  8. Angle(B, D, C) → α

AI Drawing Prompt Reference

Draw a circle, pick two opposite points on its circumference to define a diameter, then choose a third point anywhere on the circle, connect the three points to form a triangle, and measure the angle at the third point to show it is a right angle, illustrating the theorem that an angle inscribed in a semicircle is a right angle.
The prompt above was compiled from the original drawing commands and is for reference only.