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Constructing Circles Tangent to Two Circles

Constructing Circles Tangent to Two Circles
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2019-11-30 02:25
CircleCoordinate GeometryGeometric ConstructionLocus
This example demonstrates the construction of circles tangent to two given circles with adjustable centers and radii. It involves core concepts like tangent lines, circle relationships, and coordinate geometry. Key GeoGebra commands used include Point, Mirror, Circle, Midpoint, Hyperbola, Segment, and Intersect. Suitable for high school coordinate geometry learning, exploring tangent properties and locus problems.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F
  2. Point(xAxis) → G'
  3. Mirror(F, O) → F'
  4. Circle(F', G') → d_1
  5. Point(xAxis) → G
  6. Midpoint(G', G) → A'
  7. Hyperbola(F', F, A') → h
  8. Circle(F, G) → c
  9. Segment(F', G') → r'
  10. Segment(G, F) → r
  11. Mirror(G', F') → H'
  12. Mirror(G, F) → H
  13. Midpoint(H', G) → B'
  14. Hyperbola(F', F, B') → h'
  15. Mirror(A', O) → A
  16. Mirror(B', O) → B
  17. Segment(A', A) → p
  18. Segment(B', B) → p'
  19. Point(l1, t) → P
  20. Segment(P, F') → d'
  21. Segment(P, F) → d
  22. Intersect(c, d, 1) → I
  23. Mirror(I, F) → I'
  24. Intersect(d_1, d') → J, K
  25. Mirror(J, F') → J'
  26. Circle(P, I') → e
  27. Circle(P, I) → f