INSTRUCTOR PLT AND STUDENT HAVE CLOSE ENCOUNTER WITH TWIN CESSNA IN THE TFC PATTERN TURNING BASE LEG AT GCC.

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THIS WAS A TRAINING FLT. I WAS THE INSTRUCTOR WITH A STUDENT ON A DUAL XCOUNTRY FLT. MY STUDENT WAS BEHIND THE ACFT; LATE DSNDING AND BEHIND WITH CHKLISTS. HE CALLED TWR 7 MI OUT AND RPTED 7 MI NW OF THE ARPT. WE WERE MORE W THAN N; BUT I DID NOT CORRECT MY POS WITH TWR BECAUSE I FELT THE SIT DID NOT REQUIRE MORE ACCURATE RPTING. TWR TOLD US TO ENTER R BASE FOR RWY 16 AND RPT 3 MI NW. MY STUDENT READ THIS BACK CORRECTLY. MY STUDENT WAS LATE TO DSND; SO WE STARTED A RAPID DSCNT FROM 7500 FT MSL. WE RPTED 3 MI OUT AND AROUND THE SAME TIME; I HEARD THERE WAS A TWIN CESSNA ON R DOWNWIND FOR RWY 16. TWR TOLD US TO LOOK FOR THE TFC AND FOLLOW. WE RPTED WE WERE LOOKING FOR THE TFC AND ENTERING R BASE. NEXT THE TWIN CESSNA PLT CALLED THAT HE WAS DIRECTLY BELOW ME AND RECOMMENDED I TURN N. HE SAID HE WAS DIVING TO AVOID. I TOOK CTL FROM MY STUDENT; TURNED N; STOPPED OUR DSCNT AND STARTED A FULL PWR CLB. I DID NOT SEE THE TWIN-CESSNA UNTIL IT HAD PASSED BELOW ME. I NEVER RECEIVED A TFC AVOIDANCE CALL FROM TWR. TWR SAID LATER THAT HE DID NOT SEE ME UNTIL THE NEAR MISS. WE DID HAVE ALL OUR ACFT LIGHTS ON. WHEN I FINALLY SAW THE TWIN CESSNA; HE WAS 2 O'CLOCK LOW FLYING AWAY FROM ME ABOUT 1500 FT FROM ME. I HAVE NO WAY OF KNOWING FOR SURE HOW CLOSE WE CAME BECAUSE I NEVER SAW THE OTHER ACFT; BUT I ESTIMATE 500 FT VERTLY. I BELIEVE MY STUDENT'S HIGH WORKLOAD; MY HIGH WORKLOAD MANAGING HIM; DUSK LIGHTING CONDITIONS; OUR RANGE POS RPT AND RAPID DSCNT CONTRIBUTED TO THE NEAR MISS. BECAUSE OF MY STUDENT'S RAPID DSCNT; I BELIEVE WE CLOSED TO OUR 3 MI RPTING POINT FASTER THAN TWR ANTICIPATED; WHICH; ALONG WITH TWR'S INABILITY TO LOCATE MY ACFT VISUALLY; PLACED US IN A POS CLOSE TO THE TWIN CESSNA. BETTER VISUAL SCANNING; MORE ACCURATE POS RPTING; AND BETTER WORKLOAD MGMNT AS AN INSTRUCTOR COULD HAVE HELPED PREVENT THE SIT.