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National and Regional Contests
Italy Contests
Italy TST
1999 Italy TST
2
2
Part of
1999 Italy TST
Problems
(1)
Geometry inequality involving tangent to incircle
Source: Italy TST 1999
2/1/2011
Let
D
D
D
and
E
E
E
be points on sides
A
B
AB
A
B
and
A
C
AC
A
C
respectively of a triangle
A
B
C
ABC
A
BC
such that
D
E
DE
D
E
is parallel to
B
C
BC
BC
and tangent to the incircle of
A
B
C
ABC
A
BC
. Prove that
D
E
≤
1
8
(
A
B
+
B
C
+
C
A
)
DE\le\frac{1}{8}(AB+BC+CA)
D
E
≤
8
1
(
A
B
+
BC
+
C
A
)
geometry
inequalities
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