Problem 5 · 2017 Math Kangaroo
Medium
Spatial & Visual Reasoning
path-tracingspatial-reasoning
A wheel rolls along a zigzag curve as can be seen below. Which of the following pictures shows the curve that is described by the centre of the wheel?
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Answer: E
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Hint 1 of 2
The centre of the wheel can never reach into a sharp inside corner.
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Hint 2 of 2
Where the ground has a sharp point, the centre's path is rounded off.
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Approach: picture the path traced by the wheel's centre over the zigzag
- As the wheel rolls into a valley its centre cannot dip into the sharp corner, so the centre's path curves smoothly there.
- Over each peak the centre likewise rounds the corner rather than following the sharp angle.
- The picture with these rounded-off arcs over peaks and valleys is choice E.
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