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Problems
Contests
National and Regional Contests
Austria Contests
Austrian MO National Competition
1990 Federal Competition For Advanced Students, P2
3
3
Part of
1990 Federal Competition For Advanced Students, P2
Problems
(1)
inequality
Source: Austria 1990
7/10/2009
In a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
, let
E
E
E
be the intersection point of the diagonals, and let
F
1
,
F
2
,
F_1,F_2,
F
1
,
F
2
,
and
F
F
F
be the areas of
A
B
E
,
C
D
E
,
ABE,CDE,
A
BE
,
C
D
E
,
and
A
B
C
D
,
ABCD,
A
BC
D
,
respectively. Prove that: \sqrt {F_1}\plus{}\sqrt {F_2} \le \sqrt {F}.
inequalities
geometry
geometry proposed