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Contests
International Contests
Czech-Polish-Slovak Match
1996 Czech and Slovak Match
6
6
Part of
1996 Czech and Slovak Match
Problems
(1)
Nice Conditions!
Source: Czech-Slovak Match 1996
9/14/2004
The points
E
E
E
and
D
D
D
lie in the interior of sides
A
C
AC
A
C
and
B
C
BC
BC
, respectively, of a triangle
A
B
C
ABC
A
BC
. Let
F
F
F
be the intersection of the lines
A
D
AD
A
D
and
B
E
BE
BE
.Show that the area of the traingles
A
B
C
ABC
A
BC
and
A
B
F
ABF
A
BF
satisfies:
S
A
B
C
S
A
B
F
=
∣
A
C
∣
∣
A
E
∣
+
∣
B
C
∣
∣
B
D
∣
−
1
\frac{S_{ABC}}{S_{ABF}} = \frac{\mid{AC}\mid}{\mid{AE} \mid} + \frac{\mid{BC}\mid}{\mid{BD}\mid} - 1
S
A
BF
S
A
BC
=
∣
A
E
∣
∣
A
C
∣
+
∣
B
D
∣
∣
BC
∣
−
1
.
geometry
geometry solved