MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2009 National Olympiad First Round
29
29
Part of
2009 National Olympiad First Round
Problems
(1)
Cyclic quadrilateral
Source: 0
4/28/2009
P
P
P
is the intersection point of diagonals of cyclic
A
B
C
D
ABCD
A
BC
D
. The circumcenters of
△
A
P
B
\triangle APB
△
A
PB
and
△
C
P
D
\triangle CPD
△
CP
D
lie on circumcircle of
A
B
C
D
ABCD
A
BC
D
. If AC \plus{} BD \equal{} 18, then area of
A
B
C
D
ABCD
A
BC
D
is ?
<
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A
)
<
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36
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B
)
<
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81
2
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C
)
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36
3
2
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(
D
)
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81
3
4
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E
)
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None
<span class='latex-bold'>(A)</span>\ 36 \qquad<span class='latex-bold'>(B)</span>\ \frac {81}{2} \qquad<span class='latex-bold'>(C)</span>\ \frac {36\sqrt 3}{2} \qquad<span class='latex-bold'>(D)</span>\ \frac {81\sqrt 3}{4} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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(
A
)
<
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36
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(
B
)
<
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2
81
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C
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<
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2
36
3
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>
(
D
)
<
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4
81
3
<
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>
(
E
)
<
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>
None
geometry
circumcircle