1988 AJHSME Problems/Problem 24
Problem
The square in the first diagram "rolls" clockwise around the fixed regular hexagon until it reaches the bottom. In which position will the solid triangle be in diagram ?
Solution
Solution 1
The inner angle of the hexagon is , and the inner angle of the square is . Hence during each rotation the square is rotated by clockwise. In the diagram the square is therefore rotated by clockwise from its original state. Rotation by is identical to rotation by , hence the black triangle in the diagram will be pointing to the right, and the answer is .
Solution 2
Alternately, we can simply keep track of the "bottom" side of the square. In the diagrams below, this bottom side is shown in red.
See Also
1988 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
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