MathPlotAI Logo MathPlotAI

Locus of Centers of Circles Tangent to Two Circles

Locus of Centers of Circles Tangent to Two Circles
Loading the math board and drawing, please wait…
2015-11-19 13:08
CircleGeometric ConstructionLocus
In collections Conic Sections
This example demonstrates the locus of centers of all circles that are tangent to two given circles. Key concepts include the properties of circles, loci, and geometric construction. Using GeoGebra commands such as Circle, Point, Line, Intersect, etc., the dynamic changes in the locus of the centers can be explored. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Circle(A, B_1) → c
  2. Point(c) → E
  3. Line(A, E) → f
  4. Circle(E, Segment[B, D]) → e
  5. Circle(B, D) → d
  6. Segment(A, E) → a
  7. Intersect(e, f, 1) → M1
  8. LineBisector(M1, B) → b
  9. Segment(M1, B) → h
  10. Intersect(b, f) → O1
  11. Circle(O1, E) → g
  12. Segment(O1, A) → i
  13. Segment(O1, B) → j
  14. Segment(A, B) → k
  15. Intersect(d, k) → C_1,
  16. Intersect(c, k) → H,
  17. Midpoint(H, C_1) → I
  18. Intersect(g, d) → J, G, ,
  19. Segment(O1, E) → l
  20. Segment(O1, J) → m
  21. Segment(B, J) → p
  22. Angle(h, b) → α
  23. Intersect(e, f, 2) → M2
  24. LineBisector(M2, B) → r
  25. Intersect(r, f) → O2
  26. Intersect(f, l) → L
  27. Circle(O2, E) → s
  28. Intersect(s, d) → M, C, ,
  29. Segment(O2, M) → a_1
  30. Segment(O2, E) → b_1
  31. Segment(B, M) → c_1
  32. Segment(A, B) → d_1
  33. Segment(M2, B) → n
  34. Angle(n, r) → β
  35. Locus(O2, E) → loc2
  36. Locus(O1, E) → loc1
  37. Corner(1) → X1
  38. Corner(4) → X4
  39. Midpoint(X1, X4) → XX
  40. Line(XX, xAxis) → e_1
  41. Polygon(XX, (x(Corner[2]), y(XX)), Corner[3], X4) → poly1, xx, f_1, g_1, x4
  42. Midpoint(X1, XX) → XL
  43. Polygon(X1, Corner[2], (x(Corner[2]), y(XX)), XX) → poly2, h_1, i_1, j_1, k_1