\input{Klein.Angles1.tikz}
\input{Figs/Klein.Focus.tikz}

\coordinate (P1) at (P);
\coordinate (Q1) at (Q);
\coordinate (F1) at (FP);
\pgfmathparse{\RF} \let\F\pgfmathresult;

\draw [name path=s1] (P) -- (Q);
\draw [fcircle,name path=c1] (FP) circle(\R*\F);

\input{Klein.Angles2.tikz}
\input{Figs/Klein.Focus.tikz}

\coordinate (P2) at (P);
\coordinate (Q2) at (Q);
\coordinate (F2) at (FP);
\pgfmathparse{\RF} \let\G\pgfmathresult;

\draw [name path=s2] (P) -- (Q);
\draw [fcircle,name path=c2] (FP) circle(\R*\G);


\path [name intersections={of=c1 and c2,by=X}];
\fill [fcircle] (X) circle(2pt);

\path [name intersections={of=s1 and s2,by=Y}];
\fill (Y) circle(2pt);

\coordinate (P) at (P1);
\coordinate (Q) at (Q1);
\input{Figs/Klein.Cord.tikz}

\coordinate (P) at (P2);
\coordinate (Q) at (Q2);
\input{Figs/Klein.Cord.tikz}

