Problem 12 · 2023 Math Kangaroo
Medium
Geometry & Measurement
Algebra & Patterns
substitution
The diagram shows 5 equally big semicircles and the lengths of 5 distances. How big is the radius of one semicircle?
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Answer: C — 18
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Hint 1 of 2
Write the five marked distances in terms of the common radius r and the diameter 2r.
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Hint 2 of 2
Add the spans across the row so the overlaps and gaps cancel into one equation for r.
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Approach: express each labelled span in terms of r and solve
- All semicircles share radius r (diameter 2r); the labelled lengths combine spans and gaps measured along the baseline.
- Setting up the total along the row gives a linear equation in r using 22, 16, 12, 12, 22.
- Solving yields r = 18.
- So the answer is 18 (C).
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