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Serbia Contests
Serbia Team Selection Test
2017 Serbia Team Selection Test
1
1
Part of
2017 Serbia Team Selection Test
Problems
(1)
Non-stanard easy geo inequality [Serbia TST 2017, D1, P1]
Source: Serbia TST 2017, Day 1, Problem 1
5/21/2017
Let
A
B
C
ABC
A
BC
be a triangle and
D
D
D
the midpoint of the side
B
C
BC
BC
. Define points
E
E
E
and
F
F
F
on
A
C
AC
A
C
and
B
B
B
, respectively, such that
D
E
=
D
F
DE=DF
D
E
=
D
F
and
∠
E
D
F
=
∠
B
A
C
\angle EDF =\angle BAC
∠
E
D
F
=
∠
B
A
C
. Prove that
D
E
≥
A
B
+
A
C
4
.
DE\geq \frac {AB+AC} 4.
D
E
≥
4
A
B
+
A
C
.
inequalities
geometry