MathDB
AMC 8 2008 Problem 18

Source:

November 28, 2010

Problem Statement

Two circles that share the same center have radii 1010 meters and 2020 meters. An aardvark runs along the path shown, starting at AA and ending at KK. How many meters does the aardvark run? [asy] size((150)); draw((10,0)..(0,10)..(-10,0)..(0,-10)..cycle); draw((20,0)..(0,20)..(-20,0)..(0,-20)..cycle); draw((20,0)--(-20,0)); draw((0,20)--(0,-20)); draw((-2,21.5)..(-15.4, 15.4)..(-22,0), EndArrow); draw((-18,1)--(-12, 1), EndArrow); draw((-12,0)..(-8.3,-8.3)..(0,-12), EndArrow); draw((1,-9)--(1,9), EndArrow); draw((0,12)..(8.3, 8.3)..(12,0), EndArrow); draw((12,-1)--(18,-1), EndArrow); label("AA", (0,20), N); label("KK", (20,0), E); [/asy] <spanclass=latexbold>(A)</span> 10π+20<spanclass=latexbold>(B)</span> 10π+30<spanclass=latexbold>(C)</span> 10π+40<spanclass=latexbold>(D)</span> 20π+20<spanclass=latexbold>(E)</span> 20π+40 <span class='latex-bold'>(A)</span>\ 10\pi+20\qquad<span class='latex-bold'>(B)</span>\ 10\pi+30\qquad<span class='latex-bold'>(C)</span>\ 10\pi+40\qquad<span class='latex-bold'>(D)</span>\ 20\pi+20\qquad <span class='latex-bold'>(E)</span>\ 20\pi+40