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AMC8 2027 - Self-practice Set 7 Question 13

AMC8 · AMC8 2027 - Self-practice Set 7

Question 13

Triangle $ABC$ is right-angled at $B$. Each side is the diameter of a semicircle, as shown. The semicircle with diameter $AB$ has area $8\pi$, and the semicircular arc with diameter $AC$ has length $8.5\pi$. What is the radius of the semicircle with diameter $BC$?
Question illustration
  1. 7
  2. 7.5
  3. 8
  4. 8.5
  5. 9