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Guess the Circumcenter!

Guess the Circumcenter!
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2020-05-08 03:13
TriangleCircleGeometric Construction
This example demonstrates how to estimate the circumcenter of a triangle using geometric construction methods. Key math concepts include triangle, circumcircle, angle bisector, midpoint, distance, etc. Construction highlights involve GeoGebra commands like Random, Segment, Rotate, Ray, Circle, Intersect, Polygon, LineBisector, Distance, Midpoint, Angle, and If. Suitable for middle school and above students for quick formative assessment of geometric concept understanding and mastery.

GeoGebra Commands & Parameters

  1. Random(30, 150) → a
  2. Random(2, 6) → b
  3. Segment((0, 0), (b, 0)) → f
  4. Rotate(B, (a * π / 180), A) → B'
  5. Ray(A, B') → g
  6. Random(2, 6) → c
  7. Circle(A, c) → d
  8. Intersect(d, g, 1) → C
  9. Polygon(A, B, C) → t1_1, c_1, a_1, b_1
  10. LineBisector(f) → h
  11. LineBisector(a_1) → i
  12. Intersect(i, h) → D
  13. Distance(D, t2) → e
  14. LineBisector(b_1) → j
  15. Midpoint(b_1) → F
  16. Midpoint(a_1) → G
  17. Midpoint(f) → H
  18. Angle(h, f) → α
  19. Angle(i, a_1) → β
  20. Angle(j, b_1) → γ
  21. If(e ≤ 0.2, "Nice job!", 0.2 < e ≤ 1, "Pretty good!", "Not quite.") → text2