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5
5
Part of
2021 Stanford Mathematics Tournament
Problems
(1)
SMT 2021 Geometry #5
Source:
8/9/2023
Let
A
B
C
D
ABCD
A
BC
D
be a square of side length
1
1
1
, and let
E
E
E
and
F
F
F
be on the lines
A
B
AB
A
B
and
A
D
AD
A
D
, respectively, so that
B
B
B
lies between
A
A
A
and
E
E
E
, and
D
D
D
lies between
A
A
A
and
F
F
F
. Suppose that
∠
B
C
E
=
2
0
o
\angle BCE = 20^o
∠
BCE
=
2
0
o
and
∠
D
C
F
=
2
5
o
\angle DCF = 25^o
∠
D
CF
=
2
5
o
. Find the area of triangle
△
E
A
F
\vartriangle EAF
△
E
A
F
.
geometry