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Mathematics
Mathematics
Problem
Inside the unit circle
S
=
{
(
x
,
y
∣
x
2
+
y
2
=
1
)
}
S = \{(x, y | x^2 + y^2 = 1)\}
S
=
{(
x
,
y
∣
x
2
+
y
2
=
1
)}
there are three smaller circles of equal radius
a
a
a
, tangent to each other and to
S
S
S
. The value of
a
a
a
equals (a)
2
(
2
−
1
)
\sqrt{2}(\sqrt{2} - 1)
2
(
2
−
1
)
(b)
3
(
2
−
3
)
\sqrt{3}(2 - \sqrt{3})
3
(
2
−
3
)
(c)
2
(
2
−
3
)
\sqrt{2}(2 - \sqrt{3})
2
(
2
−
3
)
(d)
3
(
3
−
1
)
\sqrt{3}(\sqrt{3} - 1)
3
(
3
−
1
)
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