Question 1174259
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&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/HOW-TO-construct-a-common-exterior-tangent-line-to-two-circles.lesson>HOW TO construct a common exterior tangent line to two circles</A> 

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Find there the Figure 1b.


It represents the situation closed to that of your task.


In this Figure, &nbsp;find a right angled triangle &nbsp;(there is &nbsp;ONLY &nbsp;ONE &nbsp;UNIQUE &nbsp;such a triangle in this figure).


In this triangle, &nbsp;you are given one leg, &nbsp;which is the difference of the radii lengths  &nbsp;&nbsp;10-6 = 4 cm,

and another leg, &nbsp;whose length is equal to the portion of the rope tangent to both pulleys &nbsp;(its length is &nbsp;50 &nbsp;cm).


The distance between the centers of the pulleys is the hypotenuse of this right angled triangle.


So, &nbsp;the distance between the pulleys' centers is


    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;{{{sqrt(4^2 + 50^2)}}} = {{{sqrt(2516)}}} = 50.16 cm (rounded to two decimals after the decimal point). &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>
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Solved.