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National and Regional Contests
Bosnia Herzegovina Contests
JBMO TST - Bosnia and Herzegovina
2004 Bosnia and Herzegovina Junior BMO TST
4
4
Part of
2004 Bosnia and Herzegovina Junior BMO TST
Problems
(1)
AB / BF - AC /AE = 1, parallelogram related
Source: 2004 Bosnia & Herzegovina JBMO TST p4
5/27/2020
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram. On the ray
(
D
B
(DB
(
D
B
a point
E
E
E
is given such that the ray
(
A
B
(AB
(
A
B
is the angle bisector of
∠
C
A
E
\angle CAE
∠
C
A
E
. Let
F
F
F
be the intersection of
C
E
CE
CE
and
A
B
AB
A
B
. Prove that
A
B
B
F
−
A
C
A
E
=
1
\frac{AB}{BF} - \frac{AC}{AE} = 1
BF
A
B
−
A
E
A
C
=
1
geometry
parallelogram
angle bisector