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National and Regional Contests
Turkey Contests
National Olympiad First Round
2003 National Olympiad First Round
9
P09 [Geometry] - Turkish NMO 1st Round - 2003
P09 [Geometry] - Turkish NMO 1st Round - 2003
Source:
May 14, 2014
geometry
inradius
Problem Statement
How many integer triangles are there with inradius
1
1
1
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
0
<
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c
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a
s
s
=
′
l
a
t
e
x
−
b
o
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>
(
B
)
<
/
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a
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>
1
<
s
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a
n
c
l
a
s
s
=
′
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a
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x
−
b
o
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>
(
C
)
<
/
s
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a
n
>
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
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x
−
b
o
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>
(
D
)
<
/
s
p
a
n
>
3
<
s
p
a
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c
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a
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=
′
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a
t
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x
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b
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>
(
E
)
<
/
s
p
a
n
>
Infinite
<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ \text{Infinite}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
0
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
1
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
Infinite
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