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estudier Group Title

Circles, tangent everywhere, all the way up the triangle. Sum of perimeters of all the triangles (Bit difficult to draw this, wait a minute)

  • 2 years ago
  • 2 years ago

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  1. estudier Group Title
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    |dw:1350233869190:dw|

    • 2 years ago
  2. estudier Group Title
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    Base 20, and sides 26

    • 2 years ago
  3. estudier Group Title
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    Sum of perimeters of all the circles, I mean...

    • 2 years ago
  4. yomamabf Group Title
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    wait r u trying to teach or is this something you really need help on? cuz ur at level 99

    • 2 years ago
  5. estudier Group Title
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    Think of it as a tutorial (or not):-)

    • 2 years ago
  6. yomamabf Group Title
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    so circles dont matter so i would add 20 to 26?

    • 2 years ago
  7. estudier Group Title
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    I already corrected that above, it is the perimeter of all the circles

    • 2 years ago
  8. yomamabf Group Title
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    oh ok

    • 2 years ago
  9. estudier Group Title
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    Hint This is just Pythagorus and a splash of imagination....

    • 2 years ago
  10. experimentX Group Title
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    |dw:1350234945917:dw| is something missing ... like side of triangle or ... radius of circle of first and second??

    • 2 years ago
  11. estudier Group Title
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    Maybe you didn't see it, sorry.. I posted above "Base 20, and sides 26"

    • 2 years ago
  12. estudier Group Title
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    Maybe I should close it and repost it with out the error and including the figures :-(

    • 2 years ago
  13. klimenkov Group Title
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    No. I will solve it.

    • 2 years ago
  14. klimenkov Group Title
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    Do you have an answer?

    • 2 years ago
  15. estudier Group Title
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    Yes.

    • 2 years ago
  16. estudier Group Title
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    Wow, this a lot of typing....

    • 2 years ago
  17. estudier Group Title
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    Anyone just want to write out the infinite sum...?

    • 2 years ago
  18. klimenkov Group Title
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    Try to check my solution. Lets sign the radiuses of the circles \(r_1, r_2,...\). Then their length will be \(2\pi r_1+2\pi r_2+...=2\pi(r_1+r_2+...)\). Now watch the picture.|dw:1350235644893:dw|From the picture you can see that radiuses take a half of the height of the triangle. So I conclude that the whole perimeter of the circumferences is \(\frac 12\cdot\sqrt{26^2-10^2}=12\)

    • 2 years ago
  19. klimenkov Group Title
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    Sorry, forgot to multiply by \(2\pi\). Answer is \(24\pi\).

    • 2 years ago
  20. estudier Group Title
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    That's right, pi*(d1 + d2 +.....) = pi * altitude of triangle

    • 2 years ago
  21. CliffSedge Group Title
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    I think I've seen this done before using a geometric progression.

    • 2 years ago
  22. estudier Group Title
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    @CliffSedge Yup, u could do that, lot more work though....

    • 2 years ago
  23. estudier Group Title
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    Right, I will close this one....

    • 2 years ago
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