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Triangle and Semicircle Construction

Triangle and Semicircle Construction
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2019-03-22 00:09
TriangleCircleGeometric Construction
This example demonstrates geometric constructions involving a triangle and a semicircle, focusing on concepts like angles, area, rotation, and geometric construction. It utilizes commands such as Point, Semicircle, Segment, Midpoint, Rotate, CircleArc, Polygon, Intersect, Area, and Angle from GeoGebra. Suitable for high school students to explore geometric methods and problem-solving skills, particularly in mathematics competitions or enrichment activities.

GeoGebra Commands & Parameters

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Semicircle(A, B) → c
  3. Segment(A, B) → f
  4. Midpoint(f) → C
  5. Rotate(B, 60°, C) → B'
  6. CircleArc(C, B', A) → d
  7. Point(d) → D
  8. Rotate(D, (-(60°)), C) → D'
  9. Polygon(C, D', D) → t1, d_1, c_1, d'
  10. Intersect(Ray[A, D], Ray[B, D']) → E
  11. Polygon(D, E, D') → t2, g, d_2, e
  12. Segment(D, A) → h
  13. Segment(D', B) → i
  14. Segment(C, D) → j
  15. Segment(D', C) → k
  16. Area(Polygon[A, B, E]) → a
  17. Angle(D', C, D) → α
  18. Angle(D, D', C) → β
  19. Angle(C, D, D') → γ