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Putnam
2019 Putnam
A2
A2
Part of
2019 Putnam
Problems
(1)
Putnam 2019 A2
Source:
12/10/2019
In the triangle
△
A
B
C
\triangle ABC
△
A
BC
, let
G
G
G
be the centroid, and let
I
I
I
be the center of the inscribed circle. Let
α
\alpha
α
and
β
\beta
β
be the angles at the vertices
A
A
A
and
B
B
B
, respectively. Suppose that the segment
I
G
IG
I
G
is parallel to
A
B
AB
A
B
and that
β
=
2
tan
−
1
(
1
/
3
)
\beta = 2\tan^{-1}(1/3)
β
=
2
tan
−
1
(
1/3
)
. Find
α
\alpha
α
.
Putnam
Putnam 2019