document.write( "Question 1176256: A rope fits tightly around two pulleys . What is the distamce between the centers of the pulleys if the radii of the bigger and smaller pulleys are 10 cm and 6 cm , respectively , and the portion of the rope tangent to the pulleys is 50 cm long ? \n" ); document.write( "

Algebra.Com's Answer #802749 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "(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.

\n" ); document.write( "(2) Draw the radii of the two circles to the points of tangency.

\n" ); document.write( "(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.

\n" ); document.write( "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.

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