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2015 ASDAN Math Tournament
32
32
Part of
2015 ASDAN Math Tournament
Problems
(1)
2015 Guts #32
Source:
8/2/2022
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
=
8
AB=8
A
B
=
8
,
B
C
=
7
BC=7
BC
=
7
, and
A
C
=
11
AC=11
A
C
=
11
. Let
Γ
1
\Gamma_1
Γ
1
and
Γ
2
\Gamma_2
Γ
2
be the two possible circles that are tangent to
A
B
AB
A
B
,
A
C
AC
A
C
, and
B
C
BC
BC
when
A
C
AC
A
C
and
B
C
BC
BC
are extended, with
Γ
1
\Gamma_1
Γ
1
having the smaller radius.
Γ
1
\Gamma_1
Γ
1
and
Γ
2
\Gamma_2
Γ
2
are tangent to
A
B
AB
A
B
to
D
D
D
and
E
E
E
, respectively, and
C
E
CE
CE
intersects the perpendicular bisector of
A
B
AB
A
B
at a point
F
F
F
. What is
C
F
F
D
\tfrac{CF}{FD}
F
D
CF
?
2015
Guts Test