Problem 15 · 2020 Math Kangaroo
Hard
Spatial & Visual Reasoning
path-tracing
The figures show five paths (drawn with the thickest lines) between the points X and Y. Which of these paths is the longest?
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Answer: A
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Hint 1 of 2
Each path mixes straight segments and quarter-circle arcs; longer arcs sit on bigger circles.
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Hint 2 of 2
Add up the arc lengths: a path that uses arcs on the larger circles is longer than one on the small inner circle.
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Approach: compare total arc length of each path
- Every path combines straight pieces and circular arcs between X and Y.
- Arcs on the outer (bigger) circles are longer than arcs on the inner circles.
- Path A traces the greatest share on the larger circles, making it the longest.
Mark:
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