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Bulgarian Spring Mathematical Competition
2009 Bulgarian Spring Mathematical Competition
2009 Bulgarian Spring Mathematical Competition
Part of
Bulgarian Spring Mathematical Competition
Subcontests
(1)
Problem 10.3
1
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Spring Mathematical Tournament-Bulgaria
On the side
B
C
BC
BC
of the triangle
Δ
A
B
C
\Delta ABC
Δ
A
BC
is choosen point
K
K
K
,such that
2
∠
B
A
K
=
3
∠
K
A
C
2\angle BAK=3\angle KAC
2∠
B
A
K
=
3∠
K
A
C
.Prove that
A
B
2
A
C
3
>
A
K
5
AB^2AC^3>AK^5
A
B
2
A
C
3
>
A
K
5