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1981 IMO Shortlist
11
11
Part of
1981 IMO Shortlist
Problems
(1)
Geometric Inequality
Source:
9/15/2010
On a semicircle with unit radius four consecutive chords
A
B
,
B
C
,
C
D
,
D
E
AB,BC, CD,DE
A
B
,
BC
,
C
D
,
D
E
with lengths
a
,
b
,
c
,
d
a, b, c, d
a
,
b
,
c
,
d
, respectively, are given. Prove that
a
2
+
b
2
+
c
2
+
d
2
+
a
b
c
+
b
c
d
<
4.
a^2 + b^2 + c^2 + d^2 + abc + bcd < 4.
a
2
+
b
2
+
c
2
+
d
2
+
ab
c
+
b
c
d
<
4.
inequalities
trigonometry
geometry
Law of Sines
quadrilateral
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