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National and Regional Contests
Turkey Contests
National Olympiad First Round
2007 National Olympiad First Round
23
23
Part of
2007 National Olympiad First Round
Problems
(1)
Turkey NMO 2007 1st Round - P23 (Algebra)
Source:
10/5/2012
A unit equilateral triangle is given. Divide each side into three equal parts. Remove the equilateral triangles whose bases are middle one-third segments. Now we have a new polygon. Remove the equilateral triangles whose bases are middle one-third segments of the sides of the polygon. After repeating these steps for infinite times, what is the area of the new shape?
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None of the above
<span class='latex-bold'>(A)</span>\ \dfrac {1}{2\sqrt 3} \qquad<span class='latex-bold'>(B)</span>\ \dfrac {\sqrt 3}{8} \qquad<span class='latex-bold'>(C)</span>\ \dfrac {\sqrt 3}{10} \qquad<span class='latex-bold'>(D)</span>\ \dfrac {1}{4\sqrt 3} \qquad<span class='latex-bold'>(E)</span>\ \text{None of the above}
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None of the above
geometry