PA44 PLT AND INSTRUCTOR HAVE AN NMAC AT PRC.

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AFTER A SERIES OF TOUCH-AND-GOES ON RWY 21R; WE TOOK OFF AGAIN ON RWY 21R WITH A NORMAL CLB. AT APPROX OVER THE HWY; TWR ASKED US TO OFFSET TO THE R BY 15 DEGS. MEANWHILE; AN ACFT USING THE CALL SIGN 'ACFT Y' WAS CLRED FOR TKOF ON RWY 21L. WE AGREED TO TURN R 15 DEGS AND CONTINUED ON THE UPWIND LEG OF THE PATTERN. TWR THEN INSTRUCTED THE DEPARTING ACFT; 'ACFT Y; THE SEMINOLE AHEAD IS GOING TO OFFSET FOR YOU; OUTSIDE THAT TFC; R TURN WBOUND APPROVED.' THE PLT RESPONDED; 'R TURN WBOUND APPROVED; ACFT Y; THANKS FOR THE HELP.' ANY TIME BEFORE THESE XMISSIONS THE TWR CTLR NEVER CONFIRMED THAT THE ACFT HAD US IN SIGHT. ON OUR XWIND FOR RWY 21R; OUR ALT APPROXIMATED 5700 FT MSL. MY INSTRUCTOR RETARDED THE R ENG THROTTLE FOR SIMULATING AN ENG FAILURE; AS PART OF THE LESSON PLAN FOR THE DAY. DURING THE SECURING OF THE R ENG; WE HAD TURNED ONTO THE R DOWNWIND. NOT TOO LONG AFTER FLYING ON THE DOWNWIND; WE NOTICED A LOW WINGED; SINGLE ENG TYPE ACFT AT 2 O'CLOCK POS AND CLBING; CURRENTLY BELOW OUR ALT; WHICH WAS NOW 5800 FT MSL. MY INSTRUCTOR AND I THEN DETERMINED THAT A COLLISION WAS IMMINENT AND EVASIVE ACTION WAS NECESSARY TO AVOID AN NMAC. WE RETARDED BOTH THROTTLES AND BEGAN A RAPID DSCNT. DURING OUR MANEUVER; I DID NOT NOTICE THE OTHER ACFT CHANGE ATTITUDE OR ANY OTHER DISPLAY OF ACKNOWLEDGEMENT THAT THE PLT SAW US. OUR DSCNT ENDED AT ABOUT 5300 FT MSL (APPROX 300 FT AGL) AND WE NOTIFIED TWR OF OUR EVASIVE MANEUVER. HIS RESPONSE; 'THANK YOU; HE WAS SUPPOSED TO TURN OUTSIDE OF YOU TO THE W; I APOLOGIZE.' HE THEN XMITTED; 'ACFT Y; DID YOU HAVE THE ACFT WHEN YOU TURNED; YOU CAME A LITTLE TIGHT ON THE SEMINOLE.' ACFT Y REPLIED '(UNREADABLE)...I THOUGHT YOU SAID HE WAS OFFSETTING FOR ME.' TA'S WERE NEVER GIVEN TO ME OR THE OTHER ACFT. CTLR FAILED TO CONFIRM THAT ACFT Y HAD DEPARTING TFC IN SIGHT AND MONITOR THE SITUATION NOR CONFIRM THE INSTRUCTION GIVEN TO ACFT Y.