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9
2010 Geometry #9
2010 Geometry #9
Source:
January 2, 2024
geometry
Problem Statement
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral with an inscribed circle centered at
I
I
I
. Let
C
I
CI
C
I
intersect
A
B
AB
A
B
at
E
E
E
. If
∠
I
D
E
=
3
5
∘
\angle IDE=35^\circ
∠
I
D
E
=
3
5
∘
,
∠
A
B
C
=
7
0
∘
\angle ABC=70^\circ
∠
A
BC
=
7
0
∘
, and
∠
B
C
D
=
6
0
∘
\angle BCD=60^\circ
∠
BC
D
=
6
0
∘
, then what are all possible measures of
∠
C
D
A
\angle CDA
∠
C
D
A
?
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