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Swedish Mathematical Competition
1985 Swedish Mathematical Competition
5
5
Part of
1985 Swedish Mathematical Competition
Problems
(1)
AB+BC+CA >= 2CO, triangle in coordinate system
Source: 1985 Swedish Mathematical Competition p5
3/28/2021
In a rectangular coordinate system,
O
O
O
is the origin and
A
(
a
,
0
)
A(a,0)
A
(
a
,
0
)
,
B
(
0
,
b
)
B(0,b)
B
(
0
,
b
)
and
C
(
c
,
d
)
C(c,d)
C
(
c
,
d
)
the vertices of a triangle. Prove that
A
B
+
B
C
+
C
A
≥
2
C
O
AB+BC+CA \ge 2CO
A
B
+
BC
+
C
A
≥
2
CO
.
geometry
analytic geometry
Geometric Inequalities
inequalities