Hajj and Chag

With the world's media giving extensive and, I think, unprecedented, film coverage to the Moslem 'Hajj' (the pilgrimage to Mecca), it is worth noticing that the Arabic word 'hajj' is of course our well-known word 'chag', as featured extensively in recent Torah readings. (The 'gimel' without a dagesh used to be pronounced 'j', and still is in some Hebrew dialects.) 'Hajj' still has the connotation of 'journey / travel / pilgrimage', although the Hebrew has lost it. That is, presumably, why Moses asked Pharoah for permission to take the Israelites on 'hajj' in the desert,and why the 'Chagim' are the pilgrimage festivals to Jerusalem .... (The 'regel' in 'regalim' probably, but confusingly, doesn't have anything to do with 'feet', BTW.)