SOLUTION: The radii of two circular pulleys with their centers 10 cm apart are 3 cm and 4 cm, respectively. They are interconnected by a cross-belt so that they rotate in opposite direction
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Question 1146408: The radii of two circular pulleys with their centers 10 cm apart are 3 cm and 4 cm, respectively. They are interconnected by a cross-belt so that they rotate in opposite direction. Find the distance between two points of tangency of the two different circles measured along the belt. Answer by greenestamps(13200) (Show Source):
The problem in 2 dimensions is to find the length of an internal tangent to two circles with radii 3cm and 4cm whose centers are 10cm apart. There is a standard method for solving this general problem.
Draw the figure with the two circles, the line segment connecting the centers of the two circles, and an internal tangent.
Draw the radii of the two circles to the points of tangency.
Using the radius of the small circle and the internal tangent as two sides, form a rectangle by extending the radius of the large circle by an amount equal to the radius of the small circle. Then draw the fourth side of that rectangle.
You now have a right triangle in which the hypotenuse is the distance between the centers of the two circles (10cm) and one leg has a length equal to the sum of the radii of the two circles (7cm).
The length of the other leg is the length of the internal tangent.
ANSWER: The distance between the points of tangency of the belt with the two pulleys, measured along the belt, is sqrt(51) cm.
