1971 AHSME Problems/Problem 9
Problem 9
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
(I don't know how to use Asymptote, so if you are a visual learner, I apologize)
Let the center of the smaller circle be 
and the center of the larger circle be 
Draw perpendicular radii 
and 
The length 
should equal 24.
From 
draw a perpendicular line 
where 
is the foot of the perpendicular on Line 
Points 
and 
form a right triangle with legs 
and 
We are looking for distance 
which is 
The answer is 
-edited by coolmath34
