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\begin{tikzpicture}[scale=1]
\tkzDefPoints{0/0/A,3/0/B}
\def\coeffK{2}
\tkzApolloniusCenter[K=\coeffK](A,B)
\tkzGetPoint{P}
\tkzDefApolloniusPoint[K=\coeffK](A,B)
\tkzGetPoint{M}
\tkzDefApolloniusRadius[K=\coeffK](A,B)
\tkzDrawCircle[R,color = blue!50!black,
fill=blue!20,
opacity=.4](tkzPointResult,\tkzLengthResult pt)
\tkzDefRandPointOn[circle through= center P through M]
\tkzGetPoint{N}
\tkzDrawPoints(A,B,P,M,N)
\tkzLabelPoints(A,B,P,M,N)
\tkzDrawSegments[red](N,A N,B)
\tkzDrawPoints(A,B)
\tkzDrawSegments[red](A,B)
\tkzLabelCircle[R,draw,fill=green!10,%
text width=3cm,%
text centered](P,\tkzLengthResult pt-20pt)(-120)%
{ $MA/MB=\coeffK$\\$NA/NB=\coeffK$}
\end{tikzpicture}
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