Consider three circles: \[ \begin{array}{l} C_{1}: x^{2}+y^{2}=r^{2} \\ C_{2}:(x-1)^{2}+(y-1)^{2...

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Consider three circles:
\[
\begin{array}{l}
C_{1}: x^{2}+y^{2}=r^{2} \\
C_{2}:(x-1)^{2}+(y-1)^{2}=r^{2} \\
C_{3}:(x-2)^{2}+(y-1)^{2}=r^{2}
\end{array}
\]
- If a line \( L: y=m x+c \) be a common tangent to \( C_{1}, C_{2} \) and \( -C_{3} \) such that \( C_{1} \) and \( C_{3} \) lie on one side of line \( \mathrm{L} \) while \( C_{2} \) lies on other side, then the value of \( 20\left(r^{2}+c\right) \) is euqal to:
(a) 23
(b) 15
(c) 12
(d) 6
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