SOLUTION: A rope fits tightly around two pulleys. What is the distance between the center of the pulleys if the radii of the bigger and smaller pulleys are 10cm and 6cm, respectively,and the

Algebra ->  Circles -> SOLUTION: A rope fits tightly around two pulleys. What is the distance between the center of the pulleys if the radii of the bigger and smaller pulleys are 10cm and 6cm, respectively,and the      Log On


   

Question 1174259: A rope fits tightly around two pulleys. What is the distance between the center of the pulleys if the radii of the bigger and smaller pulleys are 10cm and 6cm, respectively,and the portion of the rope tangent to the two pulleys is 50cm long?
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

Go to the lesson
    - HOW TO construct a common exterior tangent line to two circles
in this site.

Find there the Figure 1b.

It represents the situation closed to that of your task.

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

In this triangle,  you are given one leg,  which is the difference of the radii lengths   10-6 = 4 cm,
and another leg,  whose length is equal to the portion of the rope tangent to both pulleys  (its length is  50  cm).

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

So,  the distance between the pulleys' centers is

        sqrt%284%5E2+%2B+50%5E2%29 = sqrt%282516%29 = 50.16 cm (rounded to two decimals after the decimal point).       ANSWER

Solved.