Vintage bike, new chain I've refurbished a vintage bike and I switched the old derailleur with a new medium cage tourney derailleur, the chain is also new and is 114 links long, which should be fine since me largest cog on the rear is 24 teeth and in the front is 52 teeth and distance between bb and cassette is 45cm, however, although I can shift to all gears the cage is really being stretched, is this a problem? should I try to refurbish the old worn derailleur?

see attached pics

Thanks in advance :)]3
The derailleur in the second picture does not look over extended. If the derailleur has some movement left in that position then it's OK. If it's up against the limits and is being bent then you will need to lengthen the chain.

Just for future reference, you should size a chain using a proper procedure: Thread the chain around largest sprocket and chainring (not through the derailleur), find shortest chain length with where inner and outer links, add one inner and outer link.