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India Contests
India IMO Training Camp
2010 India IMO Training Camp
10
10
Part of
2010 India IMO Training Camp
Problems
(1)
Indian Team Selection Test 2010 ST4 P1
Source:
5/23/2010
Let
A
B
C
ABC
A
BC
be a triangle. Let
Ω
\Omega
Ω
be the brocard point. Prove that
(
A
Ω
B
C
)
2
+
(
B
Ω
A
C
)
2
+
(
C
Ω
A
B
)
2
≥
1
\left(\frac{A\Omega}{BC}\right)^2+\left(\frac{B\Omega}{AC}\right)^2+\left(\frac{C\Omega}{AB}\right)^2\ge 1
(
BC
A
Ω
)
2
+
(
A
C
B
Ω
)
2
+
(
A
B
C
Ω
)
2
≥
1
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