NMAC OCCURS AT SECTOR WHILE ARTCC RADAR CTLR AT ZFW IS ENGAGED IN CONVERSATION WITH A NEW FACILITY INSTRUCTOR.

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I WAS WORKING THE MAF LOW RADAR SIDE ON MAY/XA/00 AT XA10. I HAD RELIEVED A CTLR THAT WAS BEING MONITORED BY A NEW PERSON THAT WAS TO TAKE OVER THE TRAINING FOR OUR SPECIALTY. TFC WAS LIGHT (4 ACFT) SO THIS PERSON WAS ASKING ME A LOT OF QUESTIONS ABOUT THE AREA AROUND MAF. I TOLD THE PLT OF ACFT X WHO WAS LEVEL AT 14000 FT TO DSND TO 8000 FT. ABOUT 2 MINS LATER; ACFT Y CHKED ON FREQ LEVEL 9500 FT VFR. I ISSUED TFC TO ACFT X AT 12 O'CLOCK 10 MI. ACFT X REPLIED; 'LOOKING.' I THEN ISSUED TFC TO ACFT Y; BUT DID NOT GET A REPLY. AS I WAS ABOUT TO REISSUE TFC TO ACFT Y; THE PERSON ASKED ME ANOTHER QUESTION. AFTER I ANSWERED THE QUESTION; I THEN LOOKED BACK AT THE SCOPE TO SEE THE 2 ACFT PASS. I SWITCHED ACFT X TO MAF APCH AND HE SAID 'TFC IN SIGHT' AND HE WAS NOT AT 9500 FT BUT AT 9800 FT. I ASKED THE PLT OF ACFT Y TO SAY ALT. HE SAID 9500 FT. ACFT X SWITCHED TO APCH. 7 HRS LATER; ACFT X CALLED AND WANTED TO FILE AN NMAC RPT. AFTER REVIEWING THE TAPES AND RADAR DATA; I SHOULD HAVE ISSUED A SAFETY ALERT. BUT AT THE TIME; I DID NOT THINK THE 2 ACFT WERE GOING TO BE CLOSE. THE PERSON WAS A BIG DISTR IN THIS SIT. I SHOULD HAVE TOLD HIM TO STAND BY WHILE I GOT A REPLY FROM ACFT Y.