% \usepackage{tkz-euclide}
\begin{tikzpicture}[scale=5]

  \def\sectors{18}
  \def\s{\the\numexpr\sectors-1\relax}
    \foreach \i in {0,1,2,...,\s} {
        \tkzDefPoint({\i*360/\sectors}:1){P\i}
        \tkzDefPoint({\i*360/\sectors}:1.2){PL\i}
        \tkzLabelPoint[red](PL\i){$P_{\i}$};
    }
  \tkzDefPoint(0,0){O}
  \tkzDefPoint(1.04,0){A}
  \tkzClipCircle(O,A)
    \foreach [evaluate={
              \j=int(mod(\i + 1,\sectors));
              }] \i in {0,1,2,...,\s} {
        \tkzDrawCircle[orthogonal through={P\i} and {P\j}](O,A);
        \tkzDrawPoints[color=black,fill=red,size=6](P\i);
    }
    % \tkzDefMidPoint(P1,P2) \tkzGetPoint{M}
    % \tkzDrawPoints[color=black,fill=red,size=6](M);
    % \tkzDrawArc[color=blue, delta=10](M,P2)(P1)
    % \tkzDefMidPoint(P2,P3) \tkzGetPoint{M2}
    % \tkzDrawPoints[color=black,fill=red,size=6](M2);
    % \tkzDrawArc[color=blue, delta=10](M2,P3)(P2)
\end{tikzpicture}