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Problem
Problem
Prove that
a
2
+
b
2
+
c
2
+
2
a
b
c
<
2
a^2 + b^2 + c^2 + 2abc < 2
a
2
+
b
2
+
c
2
+
2
ab
c
<
2
, where
a
,
b
,
c
a, b, c
a
,
b
,
c
are the sides of triangle
A
B
C
ABC
A
B
C
such that
a
+
b
+
c
=
2
a + b + c = 2
a
+
b
+
c
=
2
.
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