Orthogonal Circles Using TikZ

I'm making a diagram in order to explain orthogonal circles to my students. The code I'm using is as follows:

\documentclass{article}
\usepackage{tikz,tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}[scale=0.4 ]
\draw[thick, color=gray,->] (-15,0) -- (12,0) node[right] {\textcolor{black}{$x$}};
\draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {\textcolor{black}{$y$}};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=left:{$C_1$}] (C1) at (-6,4) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=right:{$C_2$}] (C2) at (2,1) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=above:{$~~A$}] (A) at (15/73,478/73) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=below:{$B~$}] (B) at (-3,-2) {};
\node at (-14, 4) {$K_1$};
\node at (9, -1) {$K_2$};
\draw[gray] (C1) -- (C2);
\draw[blue] (C1) --(B);
\draw[red] (C2) --(B);
\draw[blue] (C1) --(A);
\draw[red] (C2) --(A);
\draw (C1) circle (6.7082);
\draw (C2) circle (5.83095);
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B);
\tkzMarkSegment[color=red,pos=.5,mark=|](B,C2);
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A);
\tkzMarkSegment[color=red,pos=.5,mark=|](A,C2);
\tkzMarkRightAngle[size=0.7](C1,A,C2);
\tkzMarkRightAngle[size=0.7](C1,B,C2);
\end{tikzpicture}
\end{document}

Notice that the \tkzMarkRightAngle is at the very end of the code, which would ordinarily mean that they'd be at the very top of the diagram. However, what I get as an output is this: Notice those two mysterious black curvy lines within the right-angle sign. They're not continuations of the circles, that's for sure. I don't know what tey are. I've also tried using \tkzMarkRightAngle[fill=white] but even that wouldn't get rid of it.

• I don't understand what you mean about them being at the top of the diagram. The markings will go according to the coordinates at which you've placed the various points, won't they? – cfr Oct 24 '15 at 23:17
• I need to complete my answer but before a comment is necessary. Your problem appears here because you need to make an effort with tikito get a complete code with it. You use tkz-euclideonly to put some marks on segments and to mark right angles. I think you need to learn the answer of Harish Kumar and perhaps my answer about tkz. – Alain Matthes Feb 29 '16 at 14:37

The problem is that A and B are nodes so the connections will be draw to the point on their border which is nearest, as the crow flies, from the originating point. So the connecting point is not at the centre where you think it is.

Here's a minimised case:

\begin{tikzpicture}
[
scale=0.4,
]
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=left:{$C_1$}] (C1) at (-6,4) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=right:{$C_2$}] (C2) at (2,1) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=above:{$~~A$}] (A) at (15/73,478/73) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=below:{$B~$}] (B) at (-3,-2) {};
\tkzMarkRightAngle[size=0.7](C1,A,C2)
\tkzMarkRightAngle[size=0.7](C1,B,C2)
\end{tikzpicture}

which shows the problem: I assume cycle is used to return to the original point, which skews the final line. But this is only a guess.

To solve this, you can place a coordinate and a node, only naming the coordinate.

For example:

\documentclass[tikz,border=10pt]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}
[
scale=0.4,
my circle/.style={circle, fill=black, inner sep=0pt, minimum size=3pt}
]
\draw[thick, color=gray,->] (-15,0) -- (12,0) node[right] {$x$};
\draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {$y$};
\path [my circle]  (-6,4) coordinate (C1) node [label=left:{$C_1$}] {}
(2,1) coordinate  (C2) node [label=right:{$C_2$}] {}
(15/73,478/73) coordinate  (A) node [label=above:{$~~A$}] {}
(-3,-2) coordinate (B) node [label=below:{$B~$}] {};
\node at (-14, 4) {$K_1$};
\node at (9, -1) {$K_2$};
\draw[gray] (C1) -- (C2);
\draw[blue] (C1) --(B);
\draw[red] (C2) --(B);
\draw[blue] (C1) --(A);
\draw[red] (C2) --(A);
\draw (C1) circle (6.7082);
\draw (C2) circle (5.83095);
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B)
\tkzMarkSegment[color=red,pos=.5,mark=|](B,C2)
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A)
\tkzMarkSegment[color=red,pos=.5,mark=|](A,C2)
\tkzMarkRightAngle[size=0.7](C1,A,C2)
\tkzMarkRightAngle[size=0.7](C1,B,C2)
\end{tikzpicture}
\end{document} • ; is for tikz but not for tkz – Alain Matthes Feb 28 '16 at 22:22
• @AlainMatthes Oh. I can't read the documentation. I just copied the code from the question. ; doesn't give an error, though? What does it do? Can I remove all of them? That is, did I do it right? – cfr Feb 29 '16 at 0:54

Without tkz-euclide, only with tikz

\documentclass{article}
\usepackage[T1]{fontenc}  %% Makes | to work properly
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}[scale=0.4 ]
\draw[thick, color=gray,->] (-15,0) -- (12,0) node[right] {\textcolor{black}{$x$}};
\draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {\textcolor{black}{$y$}};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=left:{$C_1$}] (C1) at (-6,4) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=right:{$C_2$}] (C2) at (2,1) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=above:{$~~A$}] (A) at (15/73,478/73) {};
\node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=below:{$B~$}] (B) at (-3,-2) {};
\node at (-14, 4) {$K_1$};
\node at (9, -1) {$K_2$};
\draw[gray] (C1) -- (C2);
\draw[blue] (C1) -- node[sloped]{||}(B);
\draw[red] (C2) --node[sloped]{|}(B);
\draw[blue] (C1) --node[sloped]{||}(A);
\draw[red] (C2) -- node[sloped]{|}(A);
\draw (C1) circle (6.7082);
\draw (C2) circle (5.83095);

%% right angle mark
\coordinate (a) at ($(A)!8mm!45:(C1)$);
\draw (a) -- ($(A)!(a)!(C1)$);
\draw (a) -- ($(A)!(a)!(C2)$);
%% second right angle mark
\coordinate (b) at ($(B)!8mm!-45:(C1)$);
\draw (b) -- ($(B)!(b)!(C1)$);
\draw (b) -- ($(B)!(b)!(C2)$);
\end{tikzpicture}
\end{document} A "better" solution is to use the macros from tkz-euclide to define the "points". Here nodeis a bad idea like cfr explains in his answer. You don't need to use ; after a tkz command. tkz-euclideloads tikz also you can avoid to call it. I wrote better I thought that your code was with tkz-euclide but finally I realized that it was only to draw a right angle mark. Interesting with the code from tkz is the possibility to separate the definitions, the drawings and the labels. I think the code is more "readable".

A) with tkz

\documentclass{article}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}[scale=0.4]
%def
\tkzInit[xmin=-15,xmax=12,ymin=-6,ymax=12]
\tkzDrawXY[noticks]
\tkzDefPoints{-6/4/C1, 2/1/C2,0.205/6.548/A,-3/-2/B}
%drawing
\tkzDrawPoints(A,B)
\tkzDrawSegments[gray](C1,C2)
\tkzDrawSegments[red](C2,A C2,B)
\tkzDrawSegments[blue](C1,A C1,B)
\tkzDrawCircle(C1,A)
\tkzDrawCircle(C2,A)
% notation
\tkzLabelPoints(C2)
\tkzLabelPoints[left](C1)
\tkzLabelPoints[above](A)
\tkzLabelPoints[below](B)
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B)
\tkzMarkSegment[color=red,pos=.5,mark=|](B,C2)
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A)
\tkzMarkSegment[color=red,pos=.5,mark=|](A,C2)
\tkzMarkRightAngle[size=0.7](C1,A,C2)
\tkzMarkRightAngle[size=0.7](C1,B,C2)
\tkzLabelCircle[above left](C1,A)(180){$K_1$}
\tkzLabelCircle[right](C2,A)(-60){$K_2$}
\end{tikzpicture}
\end{document}

B) with tkz and tikz

Your problem comes from the definition of the points A,B,C1 etc. With tkz the definition is based on coordinate and note node. With a big figure, I think it's preferable to organize your code: 1) definition of the points 2) get some points with calculations or transformations 3) draw some lines, segments, circles etc. 4) adding some marks and labels.

\documentclass{article}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}[scale=0.4 ]
\draw[thick, color=gray,->] (-15,0) -- (12,0)node[right] {\textcolor{black}{$x$}};
\draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {\textcolor{black}{$y$}};
\coordinate[label=left:{$C_1$}] (C1) at (-6,4) {};
\coordinate[label=right:{$C_2$}] (C2) at (2,1) {};
\coordinate[label=above:{$~~A$}] (A) at (15/73,478/73) {};
\coordinate[label=below:{$B~$}] (B) at (-3,-2) {};

\draw[gray] (C1) -- (C2);
\draw[blue] (B) -- (C1) -- (A);
\draw[red]  (B) -- (C2) -- (A);

% tkz commands
\tkzDrawCircle(C1,A)
\tkzDrawCircle(C2,A)

\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B)
\tkzMarkSegment[color=red,pos=.5,mark=|](B,C2)
\tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A)
\tkzMarkSegment[color=red,pos=.5,mark=|](A,C2)
\tkzMarkRightAngle[size=0.7](C1,A,C2)
\tkzMarkRightAngle[size=0.7](C1,B,C2)
% tkz commands

\node at (-14, 4) {$K_1$};
\node at (9, -1) {$K_2$};

\fill   (A) circle (4pt)
(B) circle (4pt)
(C1) circle (4pt)
(C2) circle (4pt);
\end{tikzpicture}
\end{document}

C) with only tikz

For the right angle mark, you can use the code from Harish

%% right angle mark
\coordinate (a) at ($(A)!8mm!45:(C1)$);
\draw (a) -- ($(A)!(a)!(C1)$);
\draw (a) -- ($(A)!(a)!(C2)$);

For the circles you need a code like this

\draw (C1) let \p1 = ($(A) - (C1)$)
in
circle ({veclen(\x1,\y1)});
\draw (C2) let \p1 = ($(A) - (C2)$)
in
circle ({veclen(\x1,\y1)}); ]1

• Yay! Long time no see! Good to see you again :) – percusse Feb 28 '16 at 22:34
• (+1) But assumptions are dangerous online, you know ... – cfr Feb 29 '16 at 0:58