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496
ASU 496 All Soviet Union MO 1989 a^2+b^2 +c^2 +4abc < 1/2, perimeter 1 triangle
ASU 496 All Soviet Union MO 1989 a^2+b^2 +c^2 +4abc < 1/2, perimeter 1 triangle
Source:
August 13, 2019
geometry
perimeter
geometric inequality
inequalities
Problem Statement
A triangle with perimeter
1
1
1
has side lengths
a
,
b
,
c
a, b, c
a
,
b
,
c
. Show that
a
2
+
b
2
+
c
2
+
4
a
b
c
<
1
2
a^2 + b^2 + c^2 + 4abc <\frac 12
a
2
+
b
2
+
c
2
+
4
ab
c
<
2
1
.
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