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7
SMT 2023 Geometry #7
SMT 2023 Geometry #7
Source:
August 9, 2023
geometry
Problem Statement
Triangle
A
B
C
ABC
A
BC
has
A
C
=
5
AC = 5
A
C
=
5
.
D
D
D
and
E
E
E
are on side
B
C
BC
BC
such that
A
D
AD
A
D
and
A
E
AE
A
E
trisect
∠
B
A
C
\angle BAC
∠
B
A
C
, with
D
D
D
closer to
B
B
B
and
D
E
=
3
2
DE =\frac32
D
E
=
2
3
,
E
C
=
5
2
EC =\frac52
EC
=
2
5
. From
B
B
B
and
E
E
E
, altitudes
B
F
BF
BF
and
E
G
EG
EG
are drawn onto side
A
C
AC
A
C
. Compute
C
F
C
G
−
A
F
A
G
\frac{CF}{CG}-\frac{AF}{AG}
CG
CF
−
A
G
A
F
.
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