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International Contests
Baltic Way
2014 Baltic Way
15
15
Part of
2014 Baltic Way
Problems
(1)
Inequality in a quadrilateral
Source: Baltic Way 2014, Problem 15
11/11/2014
The sum of the angles
A
A
A
and
C
C
C
of a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is less than
18
0
∘
.
180^{\circ} .
18
0
∘
.
Prove that
A
B
⋅
C
D
+
A
D
⋅
B
C
<
A
C
(
A
B
+
A
D
)
.
AB \cdot CD + AD \cdot BC < AC(AB + AD).
A
B
⋅
C
D
+
A
D
⋅
BC
<
A
C
(
A
B
+
A
D
)
.
inequalities
triangle inequality
geometry proposed
geometry