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Hanoi Open Mathematics Competition
2012 Hanoi Open Mathematics Competitions
8
Q8 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Q8 - Hanoi Open Mathematical Olympiad 2012 - Junior Section
Source:
June 10, 2012
Problem Statement
Q8. Given a triangle
A
B
C
ABC
A
BC
and
2
2
2
point
K
∈
A
B
,
N
∈
B
C
K \in AB, \; N \in BC
K
∈
A
B
,
N
∈
BC
such that
B
K
=
2
A
K
,
C
N
=
2
B
N
BK=2AK, \; CN=2BN
B
K
=
2
A
K
,
CN
=
2
BN
and
Q
Q
Q
is the common point of
A
N
AN
A
N
and
C
K
CK
C
K
. Compute
S
△
A
B
C
S
△
B
C
Q
.
\dfrac{ S_{ \triangle ABC}}{S_{\triangle BCQ}}.
S
△
BCQ
S
△
A
BC
.
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