A C172 PLT AND INSTRUCTOR PRACTICING MANEUVERS WITH RA'S RPTS A NEAR MISS WITH AN ACFT NOT RPTED AS TFC BY ATC.

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I WAS WITH MY INSTRUCTOR ON A TRAINING FLT TO REVIEW VARIOUS PVT AND COMMERCIAL LEVEL MANEUVERS. AT THE TIME WE WERE RECEIVING RADAR TA'S FROM APCH CTL. I WAS SITTING IN THE R SEAT. WE WERE ESTABLISHED IN CRUISE FLT AFTER COMPLETING A PWR-ON STALL MANEUVER AND RECOVERY. AT THIS POINT; MY INSTRUCTOR REQUESTED TO TAKE THE CTLS. AFTER POSITIVE EXCHANGE OF CTLS OCCURRED. WE BEGAN SCANNING TO CLR THE AREA BEFORE INITIATING CLRING TURNS. STILL IN STRAIGHT AND LEVEL; I BEGAN SCANNING BEHIND AND TO THE R OF THE ACFT. AS I TURNED MY HEAD BACK TOWARDS THE FRONT; MY INSTRUCTOR AND I BOTH CAUGHT SIGHT OF AN ACFT APCHING FROM THE L-HAND SIDE. THE ACFT WAS IN A SHALLOW CLBING L-HAND TURN AT THE TIME I FIRST SPOTTED IT AND BEGAN DIVERGING BEFORE ANY EVASIVE ACTION COULD BE TAKEN. WE ESTIMATE THE ACFT TO HAVE PASSED WITHIN 400 FT OF US. MY INSTRUCTOR QUERIED ATC AS TO WHETHER OR NOT WE WERE STILL IN RADAR CONTACT; AND APCH CONFIRMED WE WERE. AT THIS POINT; MY INSTRUCTOR RPTED THAT A NEAR MIDAIR HAD OCCURRED AND ASKED IF ANY OTHER ACFT APPEARED IN OUR VICINITY. APCH RESPONDED THAT THEY DID NOT SEE ANYONE; BUT ALSO STATED THAT BECAUSE WE WERE NEAR THE LIMIT OF THEIR RADAR RANGE; A NON-XPONDER ACFT MAY NOT BE VISIBLE. WHILE I DONT FEEL THAT WE WERE BEING COMPLACENT IN OUR TFC SCAN (IN FACT; WE WERE JUST ABOUT TO EXECUTE A CLRING MANEUVER TO GUARD AGAINST THESE KINDS OF INCIDENTS); THERE ARE STILL A FEW LESSONS THAT CAN BE TAKEN FROM THIS INCIDENT. FIRST; IT ILLUSTRATES THAT ATC FLT FOLLOWING IS NO GUARANTEE THAT OTHER ACFT WILL BE SPOTTED OR RPTED. SECOND; THE OTHER ACFT HAD PASSED RELATIVELY CLOSE TO US SEVERAL MINS BEFORE. HOWEVER; BECAUSE IT APPEARED TO BE IN STRAIGHT AND LEVEL FLT AND ENRTE TO A DEST AWAY FROM OUR AREA; I DID NOT WORRY ABOUT CONTINUING TO VISUALLY TRACK IT. WHILE IT IS SOMETIMES DIFFICULT TO DETERMINE THE INTENTIONS OF OTHER PLTS; WATCHING THE ACFT FOR A LONGER PERIOD OF TIME MAY HAVE PROVIDED A CLUE THAT THE OTHER PLT INTENDED TO MANEUVER IN THE SAME AREA. FINALLY; EVEN WHEN USING GOOD SCANNING TECHNIQUE AND CLRING TURNS; IT IS STILL POSSIBLE TO MISS ANOTHER ACFT. THIS DOES NOT IMPLY THAT CLRING TECHNIQUES ARE INEFFECTIVE. INSTEAD; IT SHOULD BE EMPHASIZED THAT ONE CAN NEVER BE LOOKING FOR OTHER ACFT TOO MUCH; NOR CAN ONE TRUST THAT THE PLT OF THE OTHER ACFT WILL SEE YOU FIRST.