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Choosing a Site in an Isosceles Estate

Choosing a Site in an Isosceles Estate
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2020-06-16 00:45
TrigonometryCoordinate GeometryProbability & StatisticsOptimizationGeometric Construction
This example demonstrates the geometric problem of selecting an optimal site for construction within an isosceles triangular estate, involving concepts like isosceles triangles, area calculation, reflection, random variables, tangent function, exponent, and cones. The construction uses GeoGebra commands such as Circle, Point, Intersect, Polygon, Line, Segment, and OrthogonalLine. It is suitable for high school and above students to explore the application of geometry and probability & statistics in optimization problems.

GeoGebra Commands & Parameters

  1. Circle(J, (4 * q)) → r_1
  2. Point(r_1) → K
  3. Circle(K, 4) → t
  4. Circle(J, 4) → s_1
  5. Intersect(t, s_1, 2) → L
  6. Polygon(L, J, K) → poly3, b, a, c
  7. Point(b) → M
  8. Line(M, a) → a_1
  9. Intersect(a_1, c) → F_1
  10. Segment(M, F_1) → b_1
  11. Point(b_1) → G_1
  12. OrthogonalLine(G_1, c) → m_2
  13. OrthogonalLine(G_1, b) → n_2
  14. OrthogonalLine(G_1, a) → p_2
  15. Intersect(n_2, b) → H_1
  16. Intersect(m_2, c) → I_1
  17. Intersect(p_2, a) → J_1
  18. Segment(G_1, H_1) → q_2
  19. Segment(G_1, I_1) → r_2
  20. Segment(G_1, J_1) → s_2
  21. Segment(L, G_1) → t_2
  22. Segment(J, G_1) → a_3
  23. Segment(G_1, K) → b_3