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2009 Stanford Mathematics Tournament
10
10
Part of
2009 Stanford Mathematics Tournament
Problems
(2)
SMT 2009 Geometry 10
Source:
12/28/2011
Right triangle
A
B
C
ABC
A
BC
is inscribed in circle
W
W
W
.
∠
C
A
B
=
65
\angle{CAB}=65
∠
C
A
B
=
65
degrees, and
∠
C
B
A
=
25
\angle{CBA}=25
∠
CB
A
=
25
degrees. The median from
C
C
C
to
A
B
AB
A
B
intersects
W
W
W
and line
D
D
D
. Line
l
1
l_1
l
1
is drawn tangent to
W
W
W
at
A
A
A
. Line
l
2
l_2
l
2
is drawn tangent to
W
W
W
at
D
D
D
. The lines
l
1
l_1
l
1
and
l
2
l_2
l
2
intersect at
P
P
P
Determine
∠
A
P
D
\angle{APD}
∠
A
P
D
geometry
SMT 2009 Team #10
Source:
1/23/2022
Evaluate
∑
n
=
2009
∞
(
n
2009
)
2
n
\sum_{n=2009}^{\infty} \frac{ {n \choose 2009}}{2^n}
∑
n
=
2009
∞
2
n
(
2009
n
)
algebra