Pilot reported an NMAC event during final approach when a holding short NORDO aircraft executed a takeoff.

Narrative

While executing a VFR approach to land at ZZZ I made calls of CTAF at 10 miles and again at 5 miles with intentions to over fly the field at 2400 AGL for a right hand teardrop entry to the pattern for runway XX. I again made 2 more calls on CTAF just before and while crossing mid field. One aircraft was visible holding short of Runway XX. Another aircraft was on an RNAV approach to runway X and announced intentions to do a circling approach to runway XX. Communication was established with the faster aircraft circling for XX and was agreed that they would pass under at pattern altitude while I was crossing at 2400AGL so they could complete their approach and land. We both made call that we had each other in sight and there was no conflict. Meanwhile the aircraft holding short took runway XX and executed a take off with no radio calls. As I rolled wings level out of my teardrop into the pattern the departing aircraft had executed a hard left turn immediately after take off and came up from my left and cut in front of me approximately 75 to 100 feet off my flight path and climbing in to my flight path. I immediately executed evasive action descending and banking to the right. The other aircraft rolled out of turn and ended up above and behind me. I made radio calls for the other aircraft in the downwind to climb immediately with no response. I descended to approximately 500 AGL and after using ADSB to verify the other traffic was climbing slowly out of the pattern and I could maintain separation I executed a left base turn and climbed back to 2100 AGL and made calls for a mid field crossing and teardrop for runway XX. Two other aircraft that had been approaching the pattern gave me some extra spacing so I could land after listening to the event on CTAF.A short while later I looked up the other aircraft on ADSB and they had changed their squawk code to 7600 to indicate a radio failure.I am not sure what else I could have done to avoid this situation. There was quite a bit of communication on the CTAF frequency and as I reflected on the event I realized that the other aircraft never announced they where holding short or their take off intentions.