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Largest and smallest circles - Iran First Round 2018, P23

Source:

March 7, 2021
geometrycircles

Problem Statement

Nadia bought a compass and after opening its package realized that the length of the needle leg is 1010 centimeters whereas the length of the pencil leg is 1616 centimeters! Assume that in order to draw a circle with this compass, the angle between the pencil leg and the paper must be at least 3030 degrees but the needle leg could be positioned at any angle with respect to the paper. Let nn be the difference between the radii of the largest and the smallest circles that Nadia can draw with this compass in centimeters. Which of the following options is closest to nn?
<spanclass=′latex−bold′>(A)</span> 6<spanclass=′latex−bold′>(B)</span> 7<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 12<spanclass=′latex−bold′>(E)</span> 20<span class='latex-bold'>(A)</span>\ 6\qquad<span class='latex-bold'>(B)</span>\ 7\qquad<span class='latex-bold'>(C)</span>\ 10 \qquad<span class='latex-bold'>(D)</span>\ 12\qquad<span class='latex-bold'>(E)</span>\ 20
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