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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
21
21
Part of
2001 National Olympiad First Round
Problems
(1)
P21 [Geometry] - Turkish NMO 1st Round - 2001
Source:
4/20/2014
Let
b
b
b
be the length of the largest diagonal and
c
c
c
be the length of the smallest diagonal of a regular nonagon with side length
a
a
a
. Which one of the followings is true?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
b
=
a
+
c
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
b
=
a
c
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
b
2
=
a
2
+
c
2
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
c
=
a
+
b
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
c
2
=
a
2
+
b
2
<span class='latex-bold'>(A)</span>\ b=\dfrac{a+c}2 \qquad<span class='latex-bold'>(B)</span>\ b=\sqrt {ac} \qquad<span class='latex-bold'>(C)</span>\ b^2=\dfrac{a^2+c^2}2 \\ <span class='latex-bold'>(D)</span>\ c=a+b \qquad<span class='latex-bold'>(E)</span>\ c^2=a^2+b^2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
b
=
2
a
+
c
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
b
=
a
c
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
b
2
=
2
a
2
+
c
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
c
=
a
+
b
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
c
2
=
a
2
+
b
2
geometry
trigonometry