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24

Part of 2003 AMC 8

Problems(1)

AMC 8 2003 Problem 24

Source:

7/23/2011
A ship travels from point A to point B along a semicircular path, centered at Island X. Then it travels along a straight path from B to C. Which of these graphs best shows the ship's distance from Island X as it moves along its course?
[asy]size(150); pair X=origin, A=(-5,0), B=(5,0), C=(0,5); draw(Arc(X, 5, 180, 360)^^B--C); dot(X); label("XX", X, NE); label("CC", C, N); label("BB", B, E); label("AA", A, W);[/asy]
<spanclass=latexbold>(A)</span><span class='latex-bold'>(A)</span> [asy] defaultpen(fontsize(7)); size(80); draw((0,16)--origin--(16,0), linewidth(0.9)); label("distance traveled", (8,0), S); label(rotate(90)*"distance to X", (0,8), W); draw(Arc((4,10), 4, 0, 180)^^(8,10)--(16,12)); [/asy]
<spanclass=latexbold>(B)</span><span class='latex-bold'>(B)</span> [asy] defaultpen(fontsize(7)); size(80); draw((0,16)--origin--(16,0), linewidth(0.9)); label("distance traveled", (8,0), S); label(rotate(90)*"distance to X", (0,8), W); draw(Arc((12,10), 4, 180, 360)^^(0,10)--(8,10)); [/asy]
<spanclass=latexbold>(C)</span><span class='latex-bold'>(C)</span> [asy] defaultpen(fontsize(7)); size(80); draw((0,16)--origin--(16,0), linewidth(0.9)); label("distance traveled", (8,0), S); label(rotate(90)*"distance to X", (0,8), W); draw((0,8)--(10,10)--(16,8)); [/asy]
<spanclass=latexbold>(D)</span><span class='latex-bold'>(D)</span> [asy] defaultpen(fontsize(7)); size(80); draw((0,16)--origin--(16,0), linewidth(0.9)); label("distance traveled", (8,0), S); label(rotate(90)*"distance to X", (0,8), W); draw(Arc((12,10), 4, 0, 180)^^(0,10)--(8,10)); [/asy]
<spanclass=latexbold>(E)</span><span class='latex-bold'>(E)</span> [asy] defaultpen(fontsize(7)); size(80); draw((0,16)--origin--(16,0), linewidth(0.9)); label("distance traveled", (8,0), S); label(rotate(90)*"distance to X", (0,8), W); draw((0,6)--(6,6)--(16,10)); [/asy]
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