SOLUTION: 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 ,

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 ?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!

(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.

(2) Draw the radii of the two circles to the points of tangency.

(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.

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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