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Problems
Contests
National and Regional Contests
Iran Contests
Iran MO (1st Round)
2018 Iran MO (1st Round)
23
23
Part of
2018 Iran MO (1st Round)
Problems
(1)
Largest and smallest circles - Iran First Round 2018, P23
Source:
3/7/2021
Nadia bought a compass and after opening its package realized that the length of the needle leg is
10
10
10
centimeters whereas the length of the pencil leg is
16
16
16
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
30
30
30
degrees but the needle leg could be positioned at any angle with respect to the paper. Let
n
n
n
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
n
n
n
?
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A
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6
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B
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7
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C
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10
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D
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12
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E
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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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6
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B
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7
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C
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<
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10
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D
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12
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E
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20
geometry
circles