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2012 CHMMC Fall
2
2012 Fall Team #2
2012 Fall Team #2
Source:
March 20, 2022
geometry
Problem Statement
Consider a triangle
A
B
C
ABC
A
BC
with points
D
D
D
on
A
B
AB
A
B
,
E
E
E
on
B
C
BC
BC
, and let
F
F
F
be the intersection of
A
E
AE
A
E
and
C
D
CD
C
D
. Suppose
A
D
=
1
AD = 1
A
D
=
1
,
D
B
=
2
DB = 2
D
B
=
2
,
B
E
=
1
BE = 1
BE
=
1
,
E
C
=
3
EC = 3
EC
=
3
, and
C
A
=
5
CA = 5
C
A
=
5
. Find the value of the area of
E
C
F
ECF
ECF
minus the area of
A
D
F
ADF
A
D
F
.
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