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estudier
 3 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)
estudier
 3 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)

This Question is Closed

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Sum of perimeters of all the circles, I mean...

yomamabf
 3 years ago
Best ResponseYou've already chosen the best response.0wait r u trying to teach or is this something you really need help on? cuz ur at level 99

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Think of it as a tutorial (or not):)

yomamabf
 3 years ago
Best ResponseYou've already chosen the best response.0so circles dont matter so i would add 20 to 26?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0I already corrected that above, it is the perimeter of all the circles

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Hint This is just Pythagorus and a splash of imagination....

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1350234945917:dw is something missing ... like side of triangle or ... radius of circle of first and second??

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe you didn't see it, sorry.. I posted above "Base 20, and sides 26"

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Maybe I should close it and repost it with out the error and including the figures :(

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.3Do you have an answer?

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Wow, this a lot of typing....

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Anyone just want to write out the infinite sum...?

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.3Try 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:dwFrom 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 \(\frac 12\cdot\sqrt{26^210^2}=12\)

klimenkov
 3 years ago
Best ResponseYou've already chosen the best response.3Sorry, forgot to multiply by \(2\pi\). Answer is \(24\pi\).

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0That's right, pi*(d1 + d2 +.....) = pi * altitude of triangle

CliffSedge
 3 years ago
Best ResponseYou've already chosen the best response.0I think I've seen this done before using a geometric progression.

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0@CliffSedge Yup, u could do that, lot more work though....

estudier
 3 years ago
Best ResponseYou've already chosen the best response.0Right, I will close this one....
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