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Problem 135

AMC 10/12, early questions

Geometry Difficulty 3.4 Find the answer

Two circles that share the same center have radii $10$ meters and $20$ meters. An aardvark runs along the path shown, starting at $A$ and ending at $K$ . How many meters does the aardvark run?

Pick one

Official solution

We will deal with this part by part:
Part 1: 1/4 circumference of big circle= $\frac{2\pi r}{4}=\frac{\pi r}{2}=\frac{20\pi}{2}=10\pi$
Part 2: Big radius minus small radius= $20-10=10$
Part 3: 1/4 circumference of small circle= $\frac{\pi r}{2}=\frac{10\pi}{2}=5\pi$
Part 4: Diameter of small circle: $2*10=20$
Part 5: Same as part 3: $5\pi$
Part 6: Same as part 2: $10$
Total: $10\pi + 10 + 5\pi + 20 + 5\pi + 10 = \boxed{E = 20\pi + 40}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.