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Area of Squares Inside Circle

Area of Squares Inside Circle
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2019-09-01 17:18
CirclePolygonGeometric Construction
This example demonstrates constructing squares inside a circle and calculating their areas. Key mathematical concepts include geometry and proofs. Using GeoGebra commands such as Circle, PointIn, OrthogonalLine, Rotate, Intersect, and Polygon, a model of squares inside a circle can be constructed. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, r - 0.01) → c'
  2. Circle(A, r) → c
  3. PointIn(c') → B
  4. OrthogonalLine(B, xAxis) → v
  5. Rotate(v, (3 * π / 4), B) → v'
  6. OrthogonalLine(B, yAxis) → h
  7. Rotate(h, (3 * π / 4), B) → h'
  8. Intersect(c, h, 1) → D
  9. Intersect(c, v, 1) → C
  10. Intersect(c, h', 2) → I
  11. OrthogonalLine(I, v) → n
  12. OrthogonalLine(I, n) → d
  13. Intersect(d, h) → R
  14. Intersect(v, n) → N
  15. Intersect(c, v, 2) → E
  16. Intersect(c, v', 1) → J
  17. OrthogonalLine(J, v) → m
  18. Intersect(v, m) → O
  19. OrthogonalLine(J, h) → i
  20. Intersect(h, i) → Q
  21. Intersect(c, h', 1) → G
  22. OrthogonalLine(G, v) → l
  23. OrthogonalLine(G, l) → q
  24. Intersect(c, v', 2) → H
  25. OrthogonalLine(H, h) → j
  26. Intersect(c, h, 2) → F
  27. OrthogonalLine(H, j) → k
  28. Intersect(v, l) → K
  29. Intersect(v, k) → L
  30. Intersect(h, j) → M
  31. Intersect(h, q) → P
  32. Polygon(P, B, K, G) → q1, p, b, k_1, g_1
  33. Polygon(J, O, B, Q) → q3, r', s, t, a
  34. Polygon(N, I, R, B) → q4, e, f_1, i_1, j_1
  35. Polygon(B, M, H, L) → q2, b_1, m_1, h_1, l_1
  36. Centroid(q1) → S
  37. Centroid(q2) → T
  38. Centroid(q3) → U
  39. Centroid(q4) → V