2 LIGHT ACFT NEARLY COLLIDE IN THE TFC PATTERN AT APA.

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DURING A FINAL STAGE CHK FOR A PVT PLT APPLICANT (PART 61) I DIVERTED THE STUDENT TO APA FROM A POS APPROX 9 NM W OF THE ARPT. ALTHOUGH HE WAS UNFAMILIAR WITH APA HE OBTAINED ATIS AND CONTACTED TWR AND HEADED DIRECTLY FOR THE ARPT. HE WAS INSTRUCTED TO ENTER A MIDFIELD DOWNWIND FOR RWY 17R. APPROX 2 MI FROM THE FIELD THE TWR ISSUED A TFC ALERT FOR AN ACFT AT OUR 2 O'CLOCK POS MAKING A HIGH DOWNWIND ENTRY FROM THE S; WHICH HE ACKNOWLEDGED. THIS ACFT WAS NOT A FACTOR; PASSING QUICKLY ACROSS OUR FLT PATH AND AT A HIGHER ALT. A FEW MOMENTS LATER HE RECEIVED ANOTHER TFC ALERT FOR AN ACFT AT OUR 1 O'CLOCK POS; AND RESPONDED THAT WE WERE 'LOOKING FOR TFC.' RPTING THAT WE DID NOT YET HAVE THAT TFC IN SIGHT HE BEGAN THE TURN TO DOWNWIND APPROX MIDFIELD. I RECALL THE TWR CTLR STATING THAT THE AIRPLANE WAS NOW AT OUR 12 O'CLOCK POS; AND LESS THAN 1 MI. I WAS STILL LOOKING FOR THE TFC WHEN THE STUDENT PLT INFORMED ME THAT IT HAD JUST PASSED BENEATH US WITH NO MORE THAN 100 FT OR SO OF CLRNC. I LOOKED OVER TO THE L SIDE OF THE AIRPLANE TO SEE AN ACFT MOVING TO THE W. AT THAT TIME I RECALL THE TWR CTLR ASK AGAIN IF WE HAD THE TFC IN SIGHT AND THE STUDENT RESPONDED AFFIRMATIVELY. AT THIS TIME; SINCE THERE WAS NO FURTHER COLLISION RISK; WE CONTINUED THE DOWNWIND LEG AND WERE CLRED FOR TOUCH AND GOES ON RWY 17R. THE STUDENT WAS SHAKEN UP BY THE EXPERIENCE (AS WAS I) AND HIS LNDGS REFLECTED IT. AFTER 2 OR 3 TOUCH AND GOES WE DEPARTED THE FIELD TO THE W TO CONTINUE THE STAGE CHK BEFORE RETURNING TO BJC. I REGRET THAT I DID NOT COMMENT TO THE TWR CTLR THAT AN NMAC HAD OCCURRED AND THAT I WISHED TO RPT IT. THE TWR CTLR MADE NO FURTHER COMMENTS ABOUT THE INCIDENT ALTHOUGH HE MUST HAVE BEEN AWARE THAT THE 2 AIRPLANES HAD COME VERY CLOSE TO EACH OTHER SINCE WE WERE ALMOST ABEAM THE TWR CAB WHEN IT OCCURRED. I HAVE GIVEN CONSIDERABLE THOUGHT TO MY INACTION IN THIS MATTER AND WONDERED WHY I WASN'T MORE PROACTIVE FROM THE MOMENT TWR ALERTED US TO THE TFC. SOME REASONS MIGHT BE: 1) I COULD NOT CONCEIVE HOW ANOTHER AIRPLANE COULD BE APCHING US DIRECTLY FROM THE E; GIVEN OUR POS ON THE DOWNWIND ENTRY. THAT WOULD BE A MANEUVER TOTALLY FOREIGN TO ME AT BJC WHICH HAS VERY SIMILAR RWY LAYOUTS AND TFC PATTERNS. 2) I (AND OTHERS) HAVE THE NOTION THAT THE APA CTLRS ARE SUPERIOR TO THOSE AT BJC AND I MIGHT HAVE ALLOWED A DEGREE OF DEFERENCE TO INFLUENCE MY RESPONSE TO THE TWR CTLR. AS PIC I SHOULD HAVE QUESTIONED THE CTLR AS TO WHERE THE OTHER AIRPLANE WAS LOCATED AND ITS DIRECTION OF FLT RELATIVE TO OURS. INSTEAD I INTERPED A PERIOD OF RADIO SILENCE AS IMPLYING THE TFC WAS NO LONGER A FACTOR. 3) I DID NOT SEE THE OTHER AIRPLANE (EVEN THOUGH I WAS STILL LOOKING FOR IT) UNTIL IT EMERGED ON THE OTHER SIDE OF THE AIRPLANE AND AWAY FROM US. SINCE IT WAS CLRLY NO LONGER A COLLISION RISK I THINK I REACTED LESS ASSERTIVELY THAN I THINK I WOULD HAVE HAD I SEEN THE OTHER AIRPLANE APCHING RAPIDLY ON MY SIDE. 4) HAVING CANCELED THIS STAGE CHK FOR WX TWICE BEFORE; I WAS HIGHLY MOTIVATED TO COMPLETE THE STAGE CHK AND RELUCTANT TO DO ANYTHING THAT MIGHT DISRUPT IT. I DO NOT RECALL ANY XMISSIONS FROM THE OTHER AIRPLANE'S PLT AND DO NOT KNOW WHETHER HE OR SHE TOOK ANY EVASIVE ACTION OR EVER HAD US IN SIGHT. I CANNOT SAY IF THE OTHER PLT WAS DOING ANYTHING CONTRARY TO ATC INSTRUCTIONS. I DO NOT BELIEVE THAT WE DID.