NMAC JUST OUTSIDE THE TFC PATTERN.

Narrative

WE HAD JUST EXECUTED A PRACTICE VOR APCH AND MISSED APCH. WE WENT OUTBOUND FROM DRK TO INTERCEPT THE LOC OUTBOUND. I WAS HAVING A BIT OF TROUBLE WITH ALT CTL AND I GOT DISTRACTED WHICH LED TO OVERSHOOTING THE OUTBOUND COURSE. THESE TROUBLES MIGHT HAVE DRAWN MY INSTRUCTOR'S ATTN INSIDE THE COCKPIT. THE CURRENT ATIS INFO WAS REQUESTING THAT ALL INBOUND ACFT AND ACFT EXECUTING PRACTICE APCHS MAINTAIN CONTACT WITH PRC TWR. WE WERE IN CONTACT WITH THE TWR. THE CONFLICTING TFC WAS NOT IN CONTACT WITH THE TWR. BOTH ACFT WERE AT EXACTLY THE SAME ALT. I WAS OUTBOUND AND THE OTHER ACFT WAS INBOUND. OUR HDGS WERE WITHIN 10 DEGS OF HEAD ON. MY INSTRUCTOR DID NOT NOTICE THE CONFLICT BEFORE IT WAS TOO LATE TO TAKE ANY EVASIVE ACTION BUT DID MAKE 1 QUICK; LOUD VERBAL OUTBURST. I LOOKED UP JUST IN TIME TO SEE THE OTHER ACFT PASS OFF OUR L WING. THE OTHER PLT DID NOT APPEAR TO BE TAKING ANY EVASIVE ACTION WHATSOEVER. IT IS POSSIBLE THAT HE NEVER EVEN SAW US. MY INSTRUCTOR THEN INFORMED THE TWR THAT THERE WAS AN INBOUND ACFT NOT ON FREQ. THE TWR ADVISED THE OTHER ACFT THAT WERE EXECUTING PRACTICE APCHS OF THE POSSIBLE CONFLICT AND THEY ALSO ASKED THE PLT TO IDENT HIMSELF. HE DID SO AND SUBSEQUENTLY MADE A LNDG WITH NO FURTHER INCIDENT. WE ALSO MADE A LNDG WITHOUT FURTHER INCIDENT.