# circle arc through two points, orthogonal to a given circle

I would like to draw a circle X, inside it two points P1 and P2 (all of these with given coordinates). Let's call Y the circle passing through P1 and P2, which is orthogonal to X. Then I would like to draw the part of Y inside X and to mark the intersections of X and Y.

• Could you please upload an image of what you want to achieve, and/or preferably a MWE showing what you have tried so far? – AboAmmar Jul 22 '20 at 15:09
• @AboAmmar sorry my computer started having problems and I wasn't able to draw it – user8268 Jul 22 '20 at 16:14
• Your question is more about math/geometry than about LaTeX, right? – Zarko Jul 22 '20 at 16:14
• @Zarko no, I can compute/construct everything without any problem, I just didn't know how to do it nicely in tikz without manually putting in the computed numbers – user8268 Jul 22 '20 at 16:17
• @AndréC thanks for the suggestion – user8268 Jul 23 '20 at 19:30

I'm not sure to understand exactly the question but perhaps you want something like this.

\documentclass{standalone}
\usepackage{tkz-euclide}

\begin{document}
\begin{tikzpicture}[scale=3]
\tkzDefPoint(0,0){O}
\tkzDefPoint(1,0){A}
\tkzDrawCircle[blue](O,A)
\tkzDefPoint(-.5,-.5){z1}
\tkzDefPoint(.5,-.25){z2}
\tkzDefCircle[orthogonal through=z1 and z2](O,A) \tkzGetPoint{B}
\tkzInterCC(O,A)(B,z1) \tkzGetPoints{C}{D}
\tkzDrawPoints[size=4](O,z1,z2,C,D,B)
\tkzClipCircle(O,A)
\tkzDrawCircle[thick,color=red](B,z1)
\end{tikzpicture}

\end{document}


You can adapt this code with only TikZ

• Thanks a lot, that's exactly what I wanted! – user8268 Jul 22 '20 at 16:15
• For my tastes I will put in background the red curve :-) +1 for all the question/answers. – Sebastiano Jul 23 '20 at 12:31
• @Sebastiano you are right ! – Alain Matthes Jul 23 '20 at 18:34
• Thank you so much for understanding. You're very good user. Greetings from the Sicily. – Sebastiano Jul 23 '20 at 18:50
• @Sebastiano I updated the code ! – Alain Matthes Jul 24 '20 at 15:46

You mean something like this?

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

\begin{document}

\begin{tikzpicture}
\path (0.6,0.8) coordinate (p) (-0.8,0.6) coordinate (q);
\node at (p) [fill,circle,inner sep=0.7pt,label=$p$]{} node at (q) [fill,circle,inner sep=0.7pt,label=$q$]{};
\path ($(p)!0.5!(q)$) coordinate (c) ($(0,0)!2!(c)$) coordinate (Y);

\draw [clip] circle(1);
\draw [blue] (Y) circle(1);
\end{tikzpicture}

\end{document}