Problem 11 · 2022 Math Kangaroo
Hard
Geometry & Measurement
perimeter
Four straight lines that intersect in one single point form eight equal angles (see diagram). Which one of the black arcs has the same length as the circumference of the little (grey) circle?
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Answer: D — D
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Hint 1 of 2
Each of the eight equal angles is 45°; an arc's length is radius times its angle.
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Hint 2 of 2
Match an arc whose (radius × angle) equals the small circle's circumference 2πr.
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Approach: match arc length to circumference (deferred to key)
- The four lines split the plane into eight 45° sectors.
- Comparing each black arc's radius and angle to the small circle's circumference picks out one arc.
- That arc is D.
Mark:
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