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Math Prize For Girls Problems
2021 Math Prize for Girls Problems
8
8
Part of
2021 Math Prize for Girls Problems
Problems
(1)
Math Prize 2021 Problem 8
Source:
9/19/2021
In
△
A
B
C
\triangle ABC
△
A
BC
, let point
D
D
D
be on
B
C
‾
\overline{BC}
BC
such that the perimeters of
△
A
D
B
\triangle ADB
△
A
D
B
and
△
A
D
C
\triangle ADC
△
A
D
C
are equal. Let point
E
E
E
be on
A
C
‾
\overline{AC}
A
C
such that the perimeters of
△
B
E
A
\triangle BEA
△
BE
A
and
△
B
E
C
\triangle BEC
△
BEC
are equal. Let point
F
F
F
be the intersection of
A
B
‾
\overline{AB}
A
B
with the line that passes through
C
C
C
and the intersection of
A
D
‾
\overline{AD}
A
D
and
B
E
‾
\overline{BE}
BE
. Given that
B
D
=
10
BD = 10
B
D
=
10
,
C
D
=
2
CD = 2
C
D
=
2
, and
B
F
/
F
A
=
3
BF/FA = 3
BF
/
F
A
=
3
, what is the perimeter of
△
A
B
C
\triangle ABC
△
A
BC
?
Math Prize for Girls