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Purple Comet Problems
2018 Purple Comet Problems
28
28
Part of
2018 Purple Comet Problems
Problems
(1)
Purple Comet 2018 HS problem 28
Source:
3/19/2020
In
△
A
B
C
\vartriangle ABC
△
A
BC
points
D
,
E
D, E
D
,
E
, and
F
F
F
lie on side
B
C
‾
\overline{BC}
BC
such that
A
D
‾
\overline{AD}
A
D
is an angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
,
A
E
‾
\overline{AE}
A
E
is a median, and
A
F
‾
\overline{AF}
A
F
is an altitude. Given that
A
B
=
154
AB = 154
A
B
=
154
and
A
C
=
128
AC = 128
A
C
=
128
, and
9
×
D
E
=
E
F
,
9 \times DE = EF,
9
×
D
E
=
EF
,
fi nd the side length
B
C
BC
BC
.
geometry