#3
More generally, close coincidences for just a single number (the ratio) are maybe not so unlikely, especially as you are looking for them (if you search lots you will find some such coincidences at random). I suggest that only multiple coincidences are worthy of mention. Of course, the more exact a coincidence is, the less likely it is to occur at random. Unfortunately, measuring off a figure is not particularly precise (as Peer 4 mentions).
[Edit: for vectorial images (pdf, postscript), I've been wondering whether a good precision measurement can't be extracted from the underlying postscript code. One would start by isolating the part of the image of interest in a program like Inkscape (Illustrator if you are rich). It might be possible then to decode the relevant drawing commands.]