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National and Regional Contests
Turkey Contests
National Olympiad First Round
2005 National Olympiad First Round
1
1
Part of
2005 National Olympiad First Round
Problems
(1)
P01 [Geometry] - Turkish NMO 1st Round - 2005
Source:
10/26/2013
The circle with radius
4
4
4
passing through
A
A
A
and
B
B
B
is tangent to the circle with radius
3
3
3
passing through
A
A
A
and
C
C
C
, where
∣
A
B
∣
=
2
|AB|=2
∣
A
B
∣
=
2
. If the line
B
C
BC
BC
is tangent to the second circle, what is
∣
B
C
∣
|BC|
∣
BC
∣
?
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7
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2
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2
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D
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4
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9
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<span class='latex-bold'>(A)</span>\ 7 \qquad<span class='latex-bold'>(B)</span>\ 2 + \dfrac{\sqrt{43}}2 \qquad<span class='latex-bold'>(C)</span>\ \dfrac 52 \qquad<span class='latex-bold'>(D)</span>\ 4 + \sqrt 9 \qquad<span class='latex-bold'>(E)</span>\ \sqrt 7
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2
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43
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5
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D
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4
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9
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7
geometry