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1991 USAMO
1
1
Part of
1991 USAMO
Problems
(1)
Minimum perimeter of a triangle
Source: USAMO 1991
10/27/2005
In triangle
A
B
C
,
\, ABC, \,
A
BC
,
angle
A
\,A\,
A
is twice angle
B
,
\,B,\,
B
,
angle
C
\,C\,
C
is obtuse, and the three side lengths
a
,
b
,
c
\,a,b,c\,
a
,
b
,
c
are integers. Determine, with proof, the minimum possible perimeter.
geometry
trigonometry
angle bisector
Law of Cosines
USAMO