1971 AHSME Problems/Problem 9
Problem
An uncrossed belt is fitted without slack around two circular pulleys with radii of inches and inches. If the distance between the points of contact of the belt with the pulleys is inches, then the distance between the centers of the pulleys in inches is
Solution
Let the center of the smaller circle be and the center of the larger circle be . Draw and , as in the diagram. We know that and are perpendicular to because is tangent to both circles. From the problem, we know .
Draw with on is a rectangle, so, knowing the radii of the circles, we see that
Points and form a right triangle with legs and We are looking for which is by the Pythagorean Theorem.
Thus, our answer is .
-edited by coolmath34
See Also
1971 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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