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2020 Individual #17

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May 1, 2022
2020 Individualgeometry

Problem Statement

A rubber band of negligible thickness encloses three pegs that lie in a perfect line, as shown. Each peg has a diameter of 44 cm, as shown. What is the length of the rubber band used, in centimeters? All pegs shown are congruent circles. [asy] size(120); draw(circle((0,0),1));draw(circle((0,2),1));draw(circle((0,4),1)); dot((0,0)^^(0,2)^^(0,4)); draw((-1,0)--(-1,4)--arc((0,4),1,180,0)--(1,4)--(1,0)--arc((0,0),1,360,180),linewidth(2)); draw((-1,0)--(1,0),dotted); label("44 cm", (-0.38,0)--(1,0), N); [/asy] <spanclass=latexbold>(A)</span>8<spanclass=latexbold>(B)</span>8+4π<spanclass=latexbold>(C)</span>16+4π<spanclass=latexbold>(D)</span>16+8π<spanclass=latexbold>(E)</span>16π<span class='latex-bold'>(A) </span>8\qquad<span class='latex-bold'>(B) </span>8+4\pi\qquad<span class='latex-bold'>(C) </span>16+4\pi\qquad<span class='latex-bold'>(D) </span>16+8\pi\qquad<span class='latex-bold'>(E) </span>16\pi