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P21 [Geometry] - Turkish NMO 1st Round - 2001

Source:

April 20, 2014
geometrytrigonometry

Problem Statement

Let bb be the length of the largest diagonal and cc be the length of the smallest diagonal of a regular nonagon with side length aa. Which one of the followings is true?
<spanclass=′latex−bold′>(A)</span> b=a+c2<spanclass=′latex−bold′>(B)</span> b=ac<spanclass=′latex−bold′>(C)</span> b2=a2+c22<spanclass=′latex−bold′>(D)</span> c=a+b<spanclass=′latex−bold′>(E)</span> c2=a2+b2 <span class='latex-bold'>(A)</span>\ b=\dfrac{a+c}2 \qquad<span class='latex-bold'>(B)</span>\ b=\sqrt {ac} \qquad<span class='latex-bold'>(C)</span>\ b^2=\dfrac{a^2+c^2}2 \\ <span class='latex-bold'>(D)</span>\ c=a+b \qquad<span class='latex-bold'>(E)</span>\ c^2=a^2+b^2
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