2015 AMC 10A Problem 14
The diagram below shows the circular face of a clock with radius cm and a circular disk with radius cm externally tangent to the clock face at o’clock. The disk has an arrow painted on it, initially pointing in the upward vertical direction. Let the disk roll clockwise around the clock face. At what point on the clock face will the disk be tangent when the arrow is next pointing in the upward vertical direction?
Answer choices
Show solution
Solution
The disk of radius rolls externally around the clock face of radius . If the point of tangency moves through central angle around the clock, the disk rotates through relative to its original direction.
The arrow next points upward when is a positive multiple of . The first time this happens is , which is one-third of the way around the clock from o’clock, namely o’clock.
Thus, C is the correct answer.