Let each of the circles,
\[
\begin{array}{l}
S_{1} \equiv x^{2}+y^{2}+4 y-1=0, \\
S_{2} \equiv x.... VIDEO
Let each of the circles,
\[
\begin{array}{l}
S_{1} \equiv x^{2}+y^{2}+4 y-1=0, \\
S_{2} \equiv x^{2}+y^{2}+6 x+y+8=0, \\
S_{3} \equiv x^{2}+y^{2}-4 x-4 y-37=0
\end{array}
\]
P
Touches the other two. Let \( \mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3} \) be the points of contact of \( S_{1} \) and \( S_{2}, S_{2} \) and \( S_{3}, S_{3} \) and \( S_{1} \) respectively and \( C_{1}, C_{2}, C_{3} \) be the centres of \( S_{1}, S_{2}, S_{3} \) respectively.
The ratio \( \frac{\operatorname{area}\left(\Delta P_{1} P_{2} P_{3}\right)}{\operatorname{area}\left(\Delta C_{1} C_{2} C_{3}\right)} \) is equal to:
(1) \( 3: 2 \)
(2) \( 2: 5 \)
(3) \( 5: 3 \)
(4) \( 2: 3 \)
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