Let A and B be two fixed points on a straight line. Two circles touch this line at A and B respectively and the tangent to each other at M, when the circles vary the locus of M is?  This question has already been asked , but I could not comprehend that answer properly, also I am not allowed to comment on that answer as I don't have 50+ reputation. I have only drawn the rough sketch but not able to go any further.
Let $A$ and $B$ be two fixed points on a fixed straight line. Two circles touch this line at $A$ and $B$ respectively and tangent to each other at $M$. When the circles vary, what does the locus of $M$ form?
miktex-makepk - PK font HieroB could not be created I am depressed, after trying to install HieroTeX with MikTex 2.9 and TeXnicenter for four weeks without succeeding. I installed hieroglf, it works perfectly, but has only 60 signs. I followed the main advices, so I created a folder texmf-Local , throwed in  the content of HieroTex3.5 and Hiero-Type1.3.1.4 , put the axmf , mf and sty files where I think they belong, put that directory  texmf- local in the path searched by Miktex, updated map and file databases fo Miktex. Still the files can be compiled but Hiero fonts are not found.  Te main errors I can detect from log are the following:   " No file egypto.sty.tex found" and  "  "miktex-makepk - PK font HieroB could not be created." and similar for other fonts Thanks Defining the Complex numbers I posted this question nearly 10 days ago, but am still really not satisfied with the answers I got, I have no prior education in abstract algebra, group theory, or other abstractions, and most of the answers I got involved defining sets, groups and other things I am unfamiliar with, my question was,  How does one know the notion of real numbers is compatible with the axioms defined for complex numbers, ie how does one know that by defining an operator '$i$' with the property that $i^2=-1$, we will not in some way contradict some statement that is an outcome of the real numbers.  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Basically is there software or hardware that works as a Bluetooth KVM switch? Stack Exchange app iPhone X optimization The Stack Exchange app doesn’t look very good on Apple’s brand new flagship phone yet.    Also the app can’t identify the device model either. (Says Unknown (iPhone 10,3))   App Version: 1.6.6.2 Device: iPhone X (iPhone10,3) OS Version: Version 11.1 (Build 15B93) Planet where humans fight for access to algae Why are swap partitions discouraged on SSD drives, are they harmful? I often read that one should not place swap partitions on a SSD drive, as this may harm the device. Is this true? Can you please explain the reason to me?  Because I otherwise would have thought that placing swap on an SSD is the best choice, as it's much faster than HDDs and therefore swapping RAM contents to the SSD is not as slow as it would be with the HDD... How do I get attention for old, unfixed bug reports and feature requests without official responses here on Meta? Why is this sentence correct?     She suggested that he go to the cinema.   I would definitely use goes instead of go. How can I obtain an 'unbalanced' grid of ggplots? Modelling population with $\frac{dP}{dt}=P(\beta - \delta P)$ To display a sensitivity analysis I want to produce a . In the plot a specific base case value is compared to the values produced after changing parameters in the model. I started from this . With this I was able to get this MWE:   \usepackage{pgf} \usepackage{tikz} \usepackage{pgfplots} \pgfplotsset{compat=newest} \usetikzlibrary{positioning} \usetikzlibrary{calc} \usetikzlibrary{intersections,backgrounds} \usetikzlibrary{decorations.pathmorphing}  \pgfplotsset{     TornadoPlot/.style={% Overall settings         width = 1\textwidth,     line width=1pt,     tick style={line width=0.8pt},     xmin = -50, xmax = 50,     xtick       = {-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50},     xticklabels = {-50, -40, -30, -20, -10, 0, 10, 20, 30, 40, 50},     xmajorgrids = true,     minor x tick num = 1,     tick align = outside,     xtick pos = left, ytick pos = left,     xbar, bar shift=0pt,     height = 7cm,     enlarge y limits = 0.1, ytick = {0,1,2,3,4,5,6},     nodes near coords={         \pgfkeys{/pgf/fpu=true}%         \pgfmathparse{\pgfplotspointmeta}%         \pgfmathprintnumber{\pgfmathresult}     },     nodes near coords align = {horizontal},     before end axis/.code={         \draw ({rel axis cs:0,0}-|{axis cs:0,0}) -- ({rel axis cs:0,1}-|{axis    cs:0,0});     }              } }  \begin{document} \begin{tikzpicture}     \begin{axis}[TornadoPlot, legend style={at={(0.975,0.25)}}]             \addplot[fill=green!40] coordinates{(-3.5,0) (-16,1) (-17.5,2) (-19,3) (-34,4) (-27,5) (-22,6)};             \addplot[fill=red!40] coordinates{(4,0) (19,1) (12.5,2) (28.5,3) (34,4) (82,5) (38,6)};             \legend{upside, downside}      \end{axis} \end{tikzpicture} \end{document}   However, one of the bars (82, 5) has a positive x value that is outside the range of the domain of the plot. 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Printing pointers in C I was trying to understand something with pointers, so I wrote this code:  #include &lt;stdio.h&gt;  int main(void) {     char s[] = "asd";     char **p = &amp;s;      printf("The value of s is: %p\n", s);     printf("The direction of s is: %p\n", &amp;s);      printf("The value of p is: %p\n", p);     printf("The direction of p is: %p\n", &amp;p);      printf("The direction of s[0] is: %p\n", &amp;s[0]);     printf("The direction of s[1] is: %p\n", &amp;s[1]);     printf("The direction of s[2] is: %p\n", &amp;s[2]);      return 0; }   When compiling it with gcc I get these warnings:  $ gcc main.c -o main-bin -ansi -pedantic -Wall -lm main.c: In function ‘main’: main.c:6: warning: initialization from incompatible pointer type main.c:9: warning: format ‘%p’ expects type ‘void *’, but argument 2 has type ‘char (*)[4]’ main.c:11: warning: format ‘%p’ expects type ‘void *’, but argument 2 has type ‘char **’ main.c:12: warning: format ‘%p’ expects type ‘void *’, but argument 2 has type ‘char ***’   (The flags for gcc are because I must be C89)  Why incompatible types of pointer? Isn't the name of an array a pointer to it's first element? So if s is a pointer to 'a', &amp;s must be a char **, no? And why do I get the other warnings? Do I have to cast the pointers with (void *) in order to print them?   And when running I get something like this:  $ ./main-bin The value of s is: 0xbfb7c860 The direction of s is: 0xbfb7c860 The value of p is: 0xbfb7c860 The direction of p is: 0xbfb7c85c The direction of s[0] is: 0xbfb7c860 The direction of s[1] is: 0xbfb7c861 The direction of s[2] is: 0xbfb7c862   How can the value of s and it's direction (and of course the value of p) be the same?