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Sharygin Geometry Olympiad
2010 Sharygin Geometry Olympiad
21
21
Part of
2010 Sharygin Geometry Olympiad
Problems
(1)
Prove that S_{ABD}+S_{ACD} > S_{BAC}+S_{BDC} (21)
Source:
10/29/2010
A given convex quadrilateral
A
B
C
D
ABCD
A
BC
D
is such that
∠
A
B
D
+
∠
A
C
D
>
∠
B
A
C
+
∠
B
D
C
.
\angle ABD + \angle ACD > \angle BAC + \angle BDC.
∠
A
B
D
+
∠
A
C
D
>
∠
B
A
C
+
∠
B
D
C
.
Prove that
S
A
B
D
+
S
A
C
D
>
S
B
A
C
+
S
B
D
C
.
S_{ABD}+S_{ACD} > S_{BAC}+S_{BDC}.
S
A
B
D
+
S
A
C
D
>
S
B
A
C
+
S
B
D
C
.
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geometric transformation
reflection
trigonometry
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