C172 INVOLVED IN NMAC WHILE IN TFC PATTERN AT UNCTLED ARPT.

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I INITIATED AN APCH TO LAND ON RWY 26. I ANNOUNCED MY POS OVER THE CTAF AS BEING 5 MI E OF THE FIELD AT 2000 FT MSL. NO OTHER TFC WAS REPORTED IN THE VICINITY. I EXTENDED THE APCH 1 MI DUE S OF THE AIRFIELD AND DSNDED TO 1500 FT MSL; AND ANNOUNCED MY POS AND INTENTION TO ENTER THE PATTERN ON A 45 DEG ANGLE FOR THE DOWNWIND LEG OF RWY 26. ROUGHLY 1/2 MI S OF THE FIELD I ENTERED THE PATTERN MIDFIELD AT THE APPROPRIATE ALT AND ANNOUNCED MY POS AS BEING DOWNWIND FOR RWY 26. NO OTHER TFC WAS REPORTED AND A VISUAL WAS TAKEN TO LOCATE ANY OTHER ACFT IN THE DIRECT VICINITY. WHEN POS 1 MI BEYOND THE RWY THRESHOLD I TURNED L BASE FOR RWY 26. UPON ROLLOUT; I APPLIED 20 DEGS FLAPS AND CONTINUED THE DSCNT TO 500 FT AGL; THEN PREPARED TO ANNOUNCE MY POS. AT THAT MOMENT ANOTHER ACFT ANNOUNCED THAT THEY WERE TURNING ON THE BASE LEG FOR RWY 26 FOR A SIMULATED ENG FAILURE LNDG. I ANNOUNCED MY POS AND SCANNED THE AREA FOR THE OTHER AIRPLANE. THE OTHER ACFT APPEARED LESS THAN 200 FT VERT DISTANCE AND 50 FT VERT DISTANCE TO MY POS; DSNDING AT A FAST RATE. UPON SIGHTING THE PLANE I TOOK EVASIVE ACTION TO AVOID A POSSIBLE MIDAIR COLLISION. ALTHOUGH I WAS AT A LOWER ALT WITH THE RIGHT-OF-WAY; I ABORTED THE LNDG AND CLBED OUT OF THE PATTERN TO A SAFER ALT AWAY FROM THE FIELD. I ANNOUNCED MY INTENTIONS; AT WHICH POINT THE OTHER ACFT RESPONDED THAT THEY APPRECIATED MY COOPERATION SO THEY COULD QUICKLY LAND AND FINISH THE STUDENT'S CHK RIDE. IT THEN BECAME APPARENT TO ME THAT A DESIGNATED FAA EXAMINER WAS ONBOARD THE OTHER ACFT. AFTER RETURNING TO THE FIELD I APCHED THE STUDENT OF THE OTHER PLANE AND ASKED IF EITHER HE OR HIS EXAMINER HAD HEARD MY RADIO XMISSIONS AND HAD ESTABLISHED A VISUAL. THE STUDENT IMPLIED THAT HE TOLD THE EXAMINER THAT ANOTHER ACFT WAS IN THE PATTERN AND TECHNICALLY HAD THE RIGHT-OF-WAY; BUT THAT IF IT WERE AN ACTUAL EMER THEY WOULD THEN HAVE THE RIGHT-OF-WAY AND COULD TAKE PRIORITY OVER THE OTHER ACFT.