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2015 ASDAN Math Tournament
27
27
Part of
2015 ASDAN Math Tournament
Problems
(1)
2015 Guts #27
Source:
8/1/2022
In triangle
A
B
C
ABC
A
BC
,
D
D
D
is a point on
A
B
AB
A
B
between
A
A
A
and
B
B
B
,
E
E
E
is a point on
A
C
AC
A
C
between
A
A
A
and
C
C
C
, and
F
F
F
is a point on
B
C
BC
BC
between
B
B
B
and
C
C
C
such that
A
F
AF
A
F
,
B
E
BE
BE
, and
C
D
CD
C
D
all meet inside
△
A
B
C
\triangle ABC
△
A
BC
at a point
G
G
G
. Given that the area of
△
A
B
C
\triangle ABC
△
A
BC
is
15
15
15
, the area of
△
A
B
E
\triangle ABE
△
A
BE
is
5
5
5
, and the area of
△
A
C
D
\triangle ACD
△
A
C
D
is
10
10
10
, compute the area of
△
A
B
F
\triangle ABF
△
A
BF
.
2015
Guts Test