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Swedish Mathematical Competition
2010 Swedish Mathematical Competition
5
5
Part of
2010 Swedish Mathematical Competition
Problems
(1)
sidelengths (a + b + c) (a + b -c) = 2b^2 and a is the largest possible side
Source: 2010 (-11) Swedish Mathematical Competition p5
9/1/2020
Consider the number of triangles where the side lengths
a
,
b
,
c
a,b,c
a
,
b
,
c
satisfy
(
a
+
b
+
c
)
(
a
+
b
ā
c
)
=
2
b
2
(a + b + c) (a + b -c) = 2b^2
(
a
+
b
+
c
)
(
a
+
b
ā
c
)
=
2
b
2
. Determine the angles in the triangle for which the angle opposite to the side with the length
a
a
a
is as big as possible.
angles
geometry
sidelengths