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Saint Petersburg Mathematical Olympiad
2011 Saint Petersburg Mathematical Olympiad
5
Area of convex quadrilatera
Area of convex quadrilatera
Source: St Petersburg Olympiad 2011, Grade 9, P5
September 15, 2017
geometry
Problem Statement
A
B
C
D
ABCD
A
BC
D
- convex quadrilateral.
∠
A
+
∠
D
=
150
,
∠
B
<
150
,
∠
C
<
150
\angle A+ \angle D=150, \angle B<150, \angle C<150
∠
A
+
∠
D
=
150
,
∠
B
<
150
,
∠
C
<
150
Prove, that area
A
B
C
D
ABCD
A
BC
D
is greater than
1
4
(
A
B
∗
C
D
+
A
B
∗
B
C
+
B
C
∗
C
D
)
\frac{1}{4}(AB*CD+AB*BC+BC*CD)
4
1
(
A
B
∗
C
D
+
A
B
∗
BC
+
BC
∗
C
D
)
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