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2016 ASDAN Math Tournament
20
20
Part of
2016 ASDAN Math Tournament
Problems
(1)
2016 Guts #20
Source:
8/14/2022
Let
A
B
C
ABC
A
BC
be a triangle such that
A
B
=
9
AB=9
A
B
=
9
,
B
C
=
6
BC=6
BC
=
6
, and
A
C
=
10
AC=10
A
C
=
10
.
2
2
2
points
D
1
,
D
2
D_1,D_2
D
1
,
D
2
are labeled on
B
C
BC
BC
such that
B
C
BC
BC
is subdivided into
3
3
3
equal segments;
4
4
4
points
E
1
,
E
2
,
…
,
E
4
E_1,E_2,\dots,E_4
E
1
,
E
2
,
…
,
E
4
are labeled on
A
C
AC
A
C
such that
A
C
AC
A
C
is subdivided into
5
5
5
equal segments; and
8
8
8
points
F
1
,
F
2
,
…
,
F
8
F_1,F_2,\dots,F_8
F
1
,
F
2
,
…
,
F
8
are labeled on
A
B
AB
A
B
such that
A
B
AB
A
B
is subdivided into
9
9
9
equal segments. All possible cevians are drawn from
A
A
A
to each
D
i
D_i
D
i
; from
B
B
B
to each
E
j
E_j
E
j
; and from
C
C
C
to each
F
k
F_k
F
k
. At how many points in the interior of
△
A
B
C
\triangle ABC
△
A
BC
do at least
2
2
2
cevians intersect?
2016
Guts Round