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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2010 Sharygin Geometry Olympiad
14
14
Part of
2010 Sharygin Geometry Olympiad
Problems
(1)
Inequality on area of a triangnle and a quadrilateral (14)
Source:
10/29/2010
We have a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
and a point
M
M
M
on its side
A
D
AD
A
D
such that
C
M
CM
CM
and
B
M
BM
BM
are parallel to
A
B
AB
A
B
and
C
D
CD
C
D
respectively. Prove that
S
A
B
C
D
≥
3
S
B
C
M
.
S_{ABCD} \geq 3 S_{BCM}.
S
A
BC
D
≥
3
S
BCM
.
Remark.
S
S
S
denotes the area function.
inequalities
geometry
geometry unsolved