Six Circle Triangle







Six Circle Triangle


Arrange 6 congruent circles of diameter d in the form of a triangle so there are 3 circles on each side (double counting the vertex circles for each side). Wrap a string around the figure ("triangle" with "rounded" corners). How long is the string?

Correct Solutions:


  1. Sorin Ionescu. Ecole Secondaire Dorval, Dorval, QC, Canada
  2. Darren Kwong. South Pasadena MS, South Pasadena, CA
  3. Tetsuya Matsuguchi. Centennial HS, Boise, ID
  4. Greg Peterson. Sir Oliver Mowat CI, Scarborough, ON, Canada
  5. Adrianl Caramaliu. I.L.Caragiale HS, Ploiesti, Romania
  6. Vasilica Caramaliu. I.L.Caragiale HS, Ploiesti, Romania
  7. Gheorghe Caramaliu. I.L.Caragiale HS, Ploiesti, Romania
  8. Daniel Labbe. Polyvalente Le Boise, Victoriaville, Quebec, Canada
  9. Joel Merritt. Merrit Homeschool, Lutz, FL
  10. Travis Stepan. Sauk Centre HS, Sauk Centre, MN
  11. Teddy Schaffer. The Westminster Schools, Atlanta, GA
  12. Kathleen Lysaught. Mannheim HS, Mannheim, Germany
  13. Justin M. Altman. Center for Arts & Sciences, Saginaw, MI
  14. Alex Lorbert. Yeshivah of Flatbush HS, Brooklyn, NY
  15. Travis Kimes. Santa Ynez HS, Solvang, CA
  16. Rhyan Adamson. Center for Arts & Sciences, Saginaw, MI
  17. Katya Permiakova. Lisgar Collegiate Institute, Ottawa, ON, Canada
  18. Craig Chasseur. Center for Arts & Sciences, Saginaw, MI
  19. Richard Heid. Lincoln Park HS, Chicago, IL
  20. Michael Moyer. The Way Home School, Carlisle, PA
  21. Alison Parker. Oviedo HS, Oviedo, FL
  22. Dan Benjamin. Lake Mary HS, Lake Mary, FL
  23. Paul Kim. Heritage Prep, Orlando, FL
  24. Josh Huckabee. Heritage Prep, Orlando, FL
  25. Bao Nguyen. Fairvale HS, Sydney, Australia
  26. Mohammed Saadullah Habib. Oviedo HS, Oviedo, FL
  27. Nathan Diehl. Maize HS, Maize, KS
  28. Justin Whitely. Cascade Christian Academy, Wenatchee, WA
  29. Huan Vo. Collins Hill HS, Suwanee, GA
  30. Mihir Fladu. Titusville HS, Titusville, FL
  31. Erin Lentz. East JHS, Hiddenite, NC
  32. Shayon Ghosh. Jackson JHS, Jackson, MS
  33. Stacy Brock. Groesbeck HS, Groesbeck, TX
  34. Kelly Walraven. L.M.H., Lancaster, PA
  35. Ashley Andrews. Cascade Christian Academy, Wenatchee, WA
  36. Steph Gibbs. Cascade Christian Academy, Wenatchee, WA
  37. Jason Brown. Cascade Christian Academy, Wenatchee, WA
  38. Amit Kakkar. Lake Highland Prep, Orlando, FL
  39. Michael Fritz. Forest HS, Ocala, FL
  40. Beth Wilson. Apollo JHS, Richardson, TX
  41. Wade Hogg. North Hopkins HS, Madisonville, KY
  42. JJ Murphy. Oblong HS, Oblong, IL
  43. Geoff Rosche. North Hopkins HS, Madisonville, KY
  44. Arthur Chang. Los Altos HS, Hacienda Heights, CA
  45. Angel Lin. Whittier Christian HS, Whittier, CA
  46. Brian Yang. Los Altos HS, Hacienda Heights, CA
  47. Frank Kuo. Los Altos HS, Hacienda Heights, CA
  48. Becky Cheng. Los Altos HS, Hacienda Heights, CA
  49. Richard Cheng. Los Altos HS, Hacienda Heights, CA
  50. Karen Malis. Santa Ynez Valley Union HS, Santa Ynez, CA
  51. Michael Vandiver. North Hopkins HS, Madisonville, KY
  52. Jack Lai. Los Altos HS, Hacienda Heights, CA
  53. Kashyap Patel. Lake Highland Prep, Orlando, FL
  54. Wojciech Lewkowicz. Lemont HS, Lemont, IL
  55. Sonal Uberoi. Santa Ynez HS, Santa Ynez, CA
  56. Tim Ott. North Hopkins HS, Madisonville, KY
  57. Mike Vandiver. North Hopkins HS, Madisonville, KY
  58. Justin Lam. College Park HS, Pleasant Hill, CA
  59. Rudy Taute. Lake Highland Prep, Orlando, FL
  60. David Barsic. Franklin Regional HS, Murrysville, PA
  61. Mikey Vandiver. North Hopkins HS, Madisonville, KY
  62. Channing Slate. North Hopkins HS, Madisonville, KY
  63. Andy Curtis. North Hopkins HS, Madisonville, KY
  64. Todd Ramsey. North Hopkins HS, Madisonville, KY
  65. Lisa Abbamonte. Walkersville HS, Walkersville, MD
  66. Kevin Beall. Walkersville HS, Walkersville, MD
  67. Joe Haller. Nevada HS, Nevada, IA
  68. C. Mallon. Hood River Valley HS, Hood River, OR
  69. Jeremy Smith. Cascade Christian Academy, Wenatchee, WA
  70. Brian Fiscus. Nevada HS, Nevada, IA
  71. Amy Lekwa. Nevada HS, Nevada, IA
  72. Eun Sik Kim. United World College of Southeast Asia, Singapore
  73. Jessica Wahlman. Red Bud HS, Red Bud, IL
  74. Derek Polk. Red Bud HS, Red Bud, IL
  75. Lani Tindall. Red Bud HS, Red Bud, IL
  76. Angie Schnieder. Red Bud HS, Red Bud, IL
  77. Michael Hotz. Benjamin Logan HS, Rushsylvania, OH
  78. Lilly Tenebruso. Monona Grove HS, Monona, WI
  79. Reid Williams. Lake Highland Prep, Orlando, FL
  80. Margaret Lauerman. Walt Whitman HS, Bethesda, MD
  81. Marshall Taylor. Moscow JHS, Moscow, ID
  82. Bianca Vollmer. Markgraefler Gymnasium, Muellheim, Germany