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7
2013 HMMT Geometry #7
2013 HMMT Geometry #7
Source:
March 3, 2024
geometry
Problem Statement
Let
A
B
C
ABC
A
BC
be an obtuse triangle with circumcenter
O
O
O
such that
∠
A
B
C
=
1
5
o
\angle ABC = 15^o
∠
A
BC
=
1
5
o
and
∠
B
A
C
>
9
0
o
\angle BAC > 90^o
∠
B
A
C
>
9
0
o
. Suppose that
A
O
AO
A
O
meets
B
C
BC
BC
at
D
D
D
, and that
O
D
2
+
O
C
⋅
D
C
=
O
C
2
OD^2 + OC \cdot DC = OC^2
O
D
2
+
OC
⋅
D
C
=
O
C
2
. Find
∠
C
\angle C
∠
C
.
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