1971 AMC 12 Problem 9

Question

An uncrossed belt is fitted without slack around two circular pulleys with radii of

14

inches and

4

inches. If the distance between the points of contact of the belt with the pulleys is

24

inches, then the distance between the centers of the pulleys in inches is:

24

2\sqrt{119}

25

26

4\sqrt{35}

Join the centers and use the difference of the radii

The center distance is the hypotenuse of a right triangle with legs

24

and

10

The common external tangent and the radii to its contact points form a right triangle whose legs are

24

and

14-4=10.

Thus the center distance is

\sqrt{24^2+10^2}=\sqrt{676}=26.

Therefore, the correct answer is D.

Problem 9 in other years