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3
2022 Geometry 3
2022 Geometry 3
Source:
March 14, 2022
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
and
A
E
F
G
AEF G
A
EFG
be unit squares such that the area of their intersection is
20
21
\frac{20}{21}
21
20
. Given that
∠
B
A
E
<
4
5
o
\angle BAE < 45^o
∠
B
A
E
<
4
5
o
,
tan
∠
B
A
E
\tan \angle BAE
tan
∠
B
A
E
can be expressed as
a
b
\frac{a}{b}
b
a
for relatively prime positive integers
a
a
a
and
b
b
b
. Compute
100
a
+
b
100a + b
100
a
+
b
.
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