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estudier

  • 2 years ago

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

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  1. estudier
    • 2 years ago
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    |dw:1350233869190:dw|

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

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

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

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

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

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

  8. yomamabf
    • 2 years ago
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    oh ok

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

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

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

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

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

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

  15. estudier
    • 2 years ago
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    Yes.

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

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

  18. klimenkov
    • 2 years ago
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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 \(\frac 12\cdot\sqrt{26^2-10^2}=12\)

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

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

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

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

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

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