[contd.]
Now the interesting bit: I read up a bit more about the letter ȝ (yogh) a couple of days ago, and now know that the sound of German "ch" is one of the ones it has been used for, along with often appearing in English words that now have a g or a y.
So we've got:
• g ~ ch in fagbok / Fachbuch
• g ~ ch in equivalents of the letter ȝ
Which doesn't imply that ȝ is the historical connection between the words, but does illustrate a similar connection appearing in two different ways.