Is there any way to make a circle knowing just two points on its diameter?

Here's the complete problem I'm trying to solve: there is a segment MN (but points M and N are calculated as an intersection of other lines so I don't know their coordinates) and I want to construct the Thales circle (to find some right angles).

I've found some code for drawing part of the circumference, so I've modified it to

\coordinate (S_MN) at ($(M)!.5!(N)$);
\draw[red] (S_MN) let \p1 = ($(N)-(S_MN)$) in  ++({veclen(\x1,\y1)},0) arc (0:360:({veclen(\x1,\y1)}););


(I'm using the calc library), but the compilation runs into errors.

!package Tikz error: + or - expected. See the tikz documentation...


(Yeah, I admit that I dont know much about the TikZ construction I've used, unfortunately.)

I've also tried to compute the radius by $(M) - (N)$ (which I've seen somewhere), but without success.

---- edit ---

(...)

BUT I think I've found the problem - I've tried to remove packages form head of the doc and check if there is a problem

-> once \usepackage[czech]{babel} package is %commented, everything runs normally

\documentclass[12pt,a4paper]{report}

\usepackage[czech]{babel}

\usepackage[cp1250]{inputenc}
\usepackage{graphicx}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{epstopdf}

\usepackage{tikz}
\usetikzlibrary{calc}
\pgfmathsetseed{\pdfuniformdeviate 10000000}

\begin{document}
\begin{tikzpicture}
\draw[style=help lines] (0,0) grid[step=1cm] (3,3);
\coordinate (M) at (2,1);
\foreach \x in {1,...,5}{
\node (N) at ({random(0,3)},{random(0,3)}) {here};
\coordinate (S_MN) at ($(M)!.5!(N)$);
\draw[red] (S_MN)
let \p1 = ($(N)-(M)$),\n1 = {0.5*veclen(\x1,\y1)} in  ++(\n1,0) arc (0:360:\n1);
}
\end{tikzpicture}
\end{document}


edit2: I've used percusse's construction with cjorssen's "update" and it worked really fine. But now I've realized one problem - how coud I find that intersection with other line I've been talking about in first post? (summary: I've circle made by your way. There is also line, say, AB, which intersects the circle in two points. How could I detect them to draw that right angle for which I'm using Thales circle? Thanks in advance

-

With tkz-euclide

\documentclass{scrartcl}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}

\begin{tikzpicture}
\tkzDefPoint(2,1){A}
\tkzDefPoint(7,3){B}
\tkzDrawCircle[diameter,fill=yellow!50](A,B)
\tkzDefMidPoint(A,B) \tkzGetPoint{O}
\tkzCalcLength[cm](O,B) \tkzGetLength{rAB}
\tkzGetRandPointOn[circle = center O radius \rAB cm]{C}
\tkzDrawPolygon[fill=red!40](A,B,C)
\tkzLabelPoints(A,B,C,O)
\tkzMarkRightAngle(A,C,B)
\end{tikzpicture}

\end{document}


-
If you want to use only tikz, you need to determine the middle of AB, and then the radius with veclen. You can use Percusse's answer. –  Alain Matthes Nov 9 '12 at 12:23
thanks but I'd like to use just Calc solution if possible. But there are problems (see lower) so I'l be possibly forced to use tkz-euclide –  Doxxik Nov 11 '12 at 15:28

I've replaced one of the points with a random node. You can use the \n registers to do a calculation and use it on the path and also you can use a circle instead of the arc but I've kept the arc so that you can distinguish your own code from mine :)

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{calc}
\pgfmathsetseed{\pdfuniformdeviate 10000000}

\begin{document}

\begin{tikzpicture}
\draw[style=help lines] (0,0) grid[step=1cm] (3,3);
\coordinate (M) at (2,1);
\foreach \x in {1,...,5}{
\node (N) at ({random(0,3)},{random(0,3)}) {here};
\coordinate (S_MN) at ($(M)!.5!(N)$);
\draw[red] (S_MN) let \p1 = ($(N)-(M)$),\n1 = {0.5*veclen(\x1,\y1)} in  ++(\n1,0) arc (0:360:\n1);
}
\end{tikzpicture}
\end{document}


M is on the coord (2,1) but the N shows up as here text at each iteration.

-
Thanks but unforutnatelly this leads to same rror (mentioned in the first post).. Respectively, it works in blanc doc but when I add it to my original work it goes to that error. (I'm adding it as new figure to avoid conflicts with other stuf). I'm using just these packages: \usepackage[cp1250]{inputenc} \usepackage{graphicx} \usepackage{amsthm} \usepackage{amsmath} \usepackage{epstopdf} and language package (with babel) and of course Tikz and Calc Any ideas why is it wrong? –  Doxxik Nov 11 '12 at 15:24
@Doxxik Without a minimal working example (MWE) I can't see why you get an error. –  percusse Nov 11 '12 at 18:14
Yeah, i'm sorry. (this comment is too short so I¨ll add it as an answer) –  Doxxik Nov 11 '12 at 19:53
@Doxxik Answers are for, well, answers to the question. You should rather edit your question to include the code. –  Torbjørn T. Nov 11 '12 at 20:04
Now I've realized one problem - how coud I find that intersection with other line I've been talking about in first post? (summary: I've circle made by your way. There is also line, say, AB, which intersects the circle in two points. How could I detect them to draw that right angle for which I'm using Thales circle? Thanks in advance –  Doxxik Nov 11 '12 at 20:57

When babel is used with the czech language, it makes - active. This makes tikz calc library unable to parse correctly the coordinates. That is why you get the error message

!package Tikz error: + or - expected. See the tikz documentation...


because tikz find a - with catcode 13 (\active) while it is looking for a - with catcode 12.

A workaround is to add \shorthandoff{-} before \begin{tikzpicture} and \shorthandon{-} after \end{tikzpicture}. Note however that you won't be able to use the babel feature related to - inside the tikzpicture.

-
thanks, now it's working! %also thanks to percusse & Alain Matthes! –  Doxxik Nov 11 '12 at 20:11