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Two Circles in a Rectangle

Two Circles in a Rectangle
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2017-11-23 19:54
CirclePolygonCoordinate GeometryParametric EquationGeometric Construction
This example demonstrates the geometric construction of two tangent circles within a rectangle. It involves core mathematical concepts such as circles, rectangles, midpoints, angle bisectors, symmetry, and parametric equations. The construction utilizes GeoGebra commands and objects like Polygon, Segment, Circle, Midpoint, AngularBisector, Intersect, OrthogonalLine, Mirror, Ray, and Point as outlined in the construction summary. It is suitable for high school geometry construction lessons or exploratory activities.

GeoGebra Commands & Parameters

  1. Polygon(A, B, D, C) → poly1, a, b, d, c
  2. Segment(A, E) → f
  3. Circle(A, E) → e
  4. Midpoint(f) → F
  5. Segment(E, A) → g
  6. Segment(G, A) → h
  7. Segment(G, E) → i
  8. Segment(E, H) → j
  9. Segment(H, A) → k
  10. AngularBisector(f, h) → l, m
  11. AngularBisector(h, i) → n, p
  12. Intersect(n, m) → I
  13. OrthogonalLine(I, h) → q
  14. Intersect(q, h) → J
  15. Circle(I, Distance[I, J]) → r
  16. Mirror(r, F) → r'
  17. Mirror(I, F) → I'
  18. Segment(I, I') → s
  19. Ray(A, E) → t
  20. Segment(K, L) → f_1
  21. Point(f_1) → N
  22. Segment(N, M) → g_1