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2000 Japan MO Finals
3
3
Part of
2000 Japan MO Finals
Problems
(1)
Inequality for 5 points in the plane
Source: Japanese MO Finals 2000
2/10/2011
Given five points
A
,
B
,
C
,
D
,
E
A,B,C,D,E
A
,
B
,
C
,
D
,
E
in a plane, no three of which are collinear, prove the inequality
A
B
+
B
C
+
C
A
+
D
E
≤
A
D
+
A
E
+
B
D
+
B
E
+
C
D
+
C
E
AB+BC+CA+DE\le AD+AE+BD+BE+CD+CE
A
B
+
BC
+
C
A
+
D
E
≤
A
D
+
A
E
+
B
D
+
BE
+
C
D
+
CE
inequalities
triangle inequality
geometry proposed
geometry