MathPlotAI Logo MathPlotAI

Locus of Centers of Two Circles Tangent Externally

Locus of Centers of Two Circles Tangent Externally
Loading the math board and drawing, please wait…
2019-07-28 01:55
CircleGeometric ConstructionLocus
This example demonstrates the locus of centers of two circles that are tangent externally. Key mathematical concepts include circle, geometry, and locus. It uses commands such as Intersect, Point, Circle, PointIn, Line, Midpoint, OrthogonalLine, Segment, Distance, and Circumference in GeoGebra. Suitable for students at middle school level and above for geometric construction.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → O
  3. Circle(O, r_1) → c
  4. PointIn(b) → C
  5. Circle(C, r_2) → d
  6. Line(O, C) → h
  7. Intersect(c, h) → D, E
  8. Intersect(d, h) → F, G
  9. Midpoint(E, F) → I
  10. Circle(I, F) → k
  11. Midpoint(O, C) → M_3
  12. OrthogonalLine(M_3, h) → p
  13. Circle(O, r_1 + Δr) → q
  14. Circle(C, r_2 + Δr) → r
  15. Intersect(r, q) → L_2, L_1, ,
  16. Segment(O, L_1) → i
  17. Segment(O, L_2) → j
  18. Segment(L_1, C) → l
  19. Segment(L_2, C) → m
  20. Intersect(d, l) → L,
  21. Intersect(d, m) → N,
  22. Intersect(c, i) → P,
  23. Intersect(c, j) → Q,
  24. Circle(L_1, P) → s
  25. Circle(L_2, Q) → t
  26. Midpoint(D, G) → M
  27. Circle(O, R) → g
  28. Circle(C, R + r_1 - r_2) → c_1
  29. Intersect(g, c_1) → M_1, M_2, ,
  30. Line(M_1, O) → f_1
  31. Intersect(c, q, 1) → H
  32. Intersect(c, q, 1) → S
  33. Intersect(c, q) → T, , ,
  34. Intersect(c, f_1) → U, V
  35. Line(M_1, C) → g_1
  36. Intersect(d, r, 1) → W
  37. Intersect(d, r) → Z, , ,
  38. Intersect(d, r, 1) → A_1
  39. Intersect(d, r, 1) → B_1
  40. Intersect(d, r, 1) → C_1
  41. Intersect(d, r, 1) → D_1
  42. Intersect(d, r, 1) → E_1
  43. Intersect(d, r, 1) → F_1
  44. Intersect(d, g_1) → G_1, H_1
  45. Circle(M_1, V) → d_1
  46. Circle(C, r_2) → e_1
  47. Line(M_2, O) → a
  48. Line(M_2, C) → i_1
  49. Intersect(c, a) → B, I_1
  50. Intersect(d, r, 1) → J_1
  51. Intersect(d, r, 1) → K_1
  52. Intersect(d, r, 1) → L_3
  53. Circle(M_2, I_1) → k_1
  54. Distance(M_1, H_1) → distanceM1H1
  55. Distance(M_1, V) → distanceM1V
  56. Circumference(c) → circumferencec
  57. PointIn(c) → Pointc
  58. Intersect(c_1, h, 1) → N_1
  59. Circle(M, G) → p_1

AI Drawing Prompt Reference

Draw two externally tangent circles and find the locus of their centers. Start by plotting the intersection of the coordinate axes, then draw a circle with one center point. Next, draw another circle with a point on the first circle as the center. Connect the centers and find the intersection points. Draw a circle with one intersection point as the center. Then, find the midpoints of the circles and draw a perpendicular line from one midpoint. Finally, draw the intersections of the enlarged circles, connect the centers to the intersections, and complete all related constructions.
The prompt above was compiled from the original drawing commands and is for reference only.