# Can someone help me doing 2 points of intersection?

i wanted to draw a cissoid curve using tikz. i managed to get this far: however, i didn't manage to add visualizations of the 2 intersecting points between the big circle and the blue line and the graph of f(x) = tx.

I would love to add something like small crosses or filled black circles to visualize the points of intersection and call them R and P (i will remove the P above the blue line eventually).

can someone help me or show me an easy way of creating visual points of intersections between the circle and the other two lines?

this is my TeX-code:

\usetikzlibrary{calc,intersections}
\tikzset{>=latex}
\usetikzlibrary{datavisualization.formats.functions}
\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}

\begin{tikzpicture}[x=2cm, y=2cm]

\draw[->] (0,0) node[pos=0, left] {$O$} -- node[pos=0.8, below right, scale=0.5] {$x=2a$}(1.25,0); %% x axis
\draw[->] (0,-0.5) -- (0,1.25); %% y axis
\draw (0.5, 0) circle (0.5); % CIRCLE

%%%%%%%%%%%%%%%%%%%%

\draw(1,-0.5)[name path=line 2, pos=0, below left] coordinate(C) -- (1,1.25)coordinate (D); %% right vertical line parralel to y
\draw (0,0)[name path=line 1, pos=0, below left] coordinate(A) -- node[pos=1.025, right, scale=0.5] {$f(x) = tx$} (1.125,1) coordinate (B); %% f(x) = tx (graph)

%%%%%%%%%%%%%%%%%%%%

\draw[line width=1pt, color=blue] (0,0) coordinate(F) .. controls (0.5,0.025) ..node[pos=1, above, scale=0.65, color=black] {$P$} (0.75,0.75) coordinate(G); % curve through P
\node[below right, scale=0.65] at (intersection of  A--B and C--D){S}; % intersection point S

\end{tikzpicture}
\end{document}


\documentclass[border = 5pt, tikz]{standalone}

\usetikzlibrary{calc,intersections}
\tikzset{>=latex}
\usetikzlibrary{datavisualization.formats.functions}
\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}

\begin{tikzpicture}[x=2cm, y=2cm]

\draw[->] (0,0) node[pos=0, left] {$O$} -- node[pos=0.8, below right, scale=0.5] {$x=2a$}(1.25,0); %% x axis
\draw[->] (0,-0.5) -- (0,1.25); %% y axis
\draw[name path = circle] (0.5, 0) circle (0.5); % CIRCLE

%%%%%%%%%%%%%%%%%%%%

\draw(1,-0.5)[name path=line 2, pos=0, below left] coordinate(C) -- (1,1.25)coordinate (D); %% right vertical line parralel to y
\draw (0,0)[name path=line 1, pos=0, below left] coordinate(A) -- node[pos=1.025, right, scale=0.5] {$f(x) = tx$} (1.125,1) coordinate (B); %% f(x) = tx (graph)

%%%%%%%%%%%%%%%%%%%%

\draw[line width=1pt, color=blue, name path = blue line] (0,0) coordinate(F) .. controls (0.5,0.025) ..node[pos=1, above, scale=0.65, color=black] {$P$} (0.75,0.75) coordinate(G); % curve through P
\node[below right, scale=0.65] at (intersection of  A--B and C--D){S}; % intersection point S

%%%%%%%%%%%%%%%%%%%% <- added this
\fill[red,name intersections={of=blue line and circle}]
(intersection-1) circle (2pt) node[below right] {R};

\fill[red,name intersections={of=line 1 and circle}]
(intersection-1) circle (2pt) node[above left] {P};

\end{tikzpicture}
\end{document} • @Zest Happy to help! – caverac Mar 20 '18 at 11:19
• i just wanted to add that your changes helped me getting behind the general syntax such that i'll be able to do it myself in the future. thanks again! i really appreciate your time and effort. – Zest Mar 20 '18 at 20:27
• @caverac I suppose you used name path=line 2 by accident on the right vertical line parallel to y. Also using below, right and above, left in the intersection nodes is like to just use right and left, respectively. Finally, I obtain the P intersection shown in the picture you uploaded using intersection-1 in the second \fill command. Using intersection-2, namely compiling the code you posted, I get the P point in the origin. Am I maybe doing something wrong? – Axel Krypton Mar 20 '18 at 20:48
• @AxelKrypton Thanks for catching that. You're right in all cases, I fixed the problems – caverac Mar 20 '18 at 21:05