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6
2015 Geometry #6
2015 Geometry #6
Source:
July 1, 2022
2015
Geometry Test
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle and let
D
D
D
be a point on
A
C
AC
A
C
. The angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
intersects
B
D
BD
B
D
at
E
E
E
and
B
C
BC
BC
at
F
F
F
. Suppose that
C
F
D
E
=
5
4
\tfrac{CF}{DE}=\tfrac{5}{4}
D
E
CF
=
4
5
and that
B
E
B
F
=
3
2
\tfrac{BE}{BF}=\tfrac{3}{2}
BF
BE
=
2
3
. What is
C
D
A
D
\tfrac{CD}{AD}
A
D
C
D
?
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