# How do you create a keyhole contour not centered at the origin?

I've been trying to create a keyhole contour where the keyhole is a tiny circle in say, the first quadrant, and the main circle is still centered at the origin. I'm specifically not trying to create a keyhole contour where the keyhole is at the origin, and can't seem to find how to do that. I've been playing around with it for a while, but can't make anything work. Does anybody have any tips?

Thanks!

Edit: Here's what I'm trying to create:

• Welcome to TeX.SX! Please could you share what you have done so far in the form of a minimal working example (MWE). This makes it easier both for us to understand what your issue is and provide solutions/suggestions. Apr 13, 2017 at 20:42
• Show us what you have been playing around! Apr 13, 2017 at 20:44
• Show us also what you wanted to achieve (a photo of an hand-written drawing could be enough), please! Apr 13, 2017 at 20:47
• @CarLaTeX I added a photo of what I'm going for (a poorly drawn one, I might add). I can't figure out how to make the keyhole look like that though, for every guide I've seen for drawing keyhole contours makes has the keyhole at the origin. Apr 14, 2017 at 0:52

Like this:

In image is considered $sin{alpha} ~ \alpha$ (at small \alpha) and ratio between angles of hole in locus is about 8:

\documentclass[tikz,
border=3mm,
]{standalone}
\usetikzlibrary{arrows.meta, decorations.markings}

\begin{document}
\begin{tikzpicture}[>=Straight Barb,
decoration={markings,% switch on markings
mark=between positions 0.2 and 0.8 step 0.25 with {\arrow[thick]{>}},
mark=at position 0.86 with {\arrow[thick]{>}},
mark=at position 0.98 with {\arrow[thick]{>}}
}]
% curve
\draw[fill=gray!10, postaction={decorate}]
(47.5:2) arc (47.5:360:2   ) arc (0:42.5:2)
-- + (225:0.5) arc (25  :0  :0.25) arc(360:65:0.25) -- cycle;
% singularity
\fill[red]  (45:1.25) circle (1pt) node[inner sep=2pt,font=\footnotesize,right] {$a$};
\draw[thick, ->] (0,0) -- node[sloped,above] {$r$} (330:2);
\draw[->] (-3,0) -- (3,0) node[right] {$\Re$};
\draw[->] (0,-3) -- (0,3) node[above] {$\Im$};

• @DavidBowman, you didn't provide anything about what you try so far nor about your document. So, with not knowing preamble of your document and \documentclass{...} I can't say anything what is going wrong at you :(. Image size is 4cm x 4cm ... Apr 14, 2017 at 3:01
• @DavidBowman Maybe, x and y are set to non-default values. Then, it helps to reset them: \begin{tikzpicture}[x=1cm, y=1cm]. Apr 14, 2017 at 4:15