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Moldova Contests
JBMO TST - Moldova
2009 Junior Balkan Team Selection Tests - Moldova
7
Prove that $BF=CD$.
Prove that $BF=CD$.
Source: Moldova JTST 2009
May 10, 2023
geometry
Problem Statement
In triangle
A
B
C
ABC
A
BC
there are points
D
∈
(
A
C
)
D\in(AC)
D
∈
(
A
C
)
and
F
∈
(
A
B
)
F\in(AB)
F
∈
(
A
B
)
such that
A
D
=
A
B
AD=AB
A
D
=
A
B
and line
B
C
BC
BC
splits the segment
[
C
F
]
[CF]
[
CF
]
in half. Prove that
B
F
=
C
D
BF=CD
BF
=
C
D
.
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