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Maximize Area of Rectangle In Semicircle

Maximize Area of Rectangle In Semicircle
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2015-06-20 01:10
TrigonometryCoordinate GeometryIntegralOptimizationGeometric Construction
This example demonstrates the geometric construction and calculation of the largest rectangle area inscribed within a semicircle. It involves core mathematical concepts such as coordinate geometry, geometric construction, optimization, and definite integrals. Key GeoGebra commands used in the construction include Circle, Line, Point, OrthogonalLine, Intersect, Polygon, Segment, Angle, and PointIn. It is suitable for high school students and math enthusiasts studying geometric optimization problems and calculus applications.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Line(A, B) → a
  3. Point(c) → X
  4. OrthogonalLine(X, a) → b
  5. Line(X, a) → d
  6. Intersect(c, d, 2) → D
  7. OrthogonalLine(D, a) → e
  8. Intersect(a, e) → E
  9. Intersect(a, b) → F
  10. Polygon(E, F, X, D) → poly1, e_1, f, c_1, d_1
  11. Segment(A, X) → g
  12. Point(a) → G
  13. Angle(G, A, X) → s
  14. PointIn(poly1) → Pointpoly1
  15. Intersect(c, a) → H, I
  16. Segment(I, H) → h