Question 1176256
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(1) Draw a sketch showing the two pulleys, the segment joining the centers of the two pulleys, and a line tangent to the two pulleys.  That tangent line represents the 50cm piece of rope between the points of tangency to the two pulleys.<br>
(2) Draw the radii of the two circles to the points of tangency.<br>
(3) Draw a segment from the center of the small circle to the radius of the larger circle, parallel to the tangent.   That segment forms a rectangle with the tangent, the radius of the small circle, and a portion of the radius of the large circle.<br>
Your sketch now shows that rectangle and a right triangle.  You know the lengths of the two legs of the right triangle; the hypotenuse is the distance between the centers of the pulleys that you are looking for.  The Pythagorean Theorem will give you the answer.<br>