NMAC IN THE TFC PATTERN BTWN A MOONEY AND A CHEROKEE AT APF; FL.

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I WAS SERVING AS FLT INSTRUCTOR IN AN M20J MOONEY. WE HAD BEEN DOING TKOFS AND LNDGS IN THE PATTERN AS PART OF TRAINING. STUDENT (OWNER OF ACFT) RPTED MIDFIELD AT 1800 FT FOR R DOWNWIND FOR RWY 5 AT NAPLES TWR. TWR RESPONDED WITH 'ROGER.' ALMOST IMMEDIATELY AFTERWARDS; I LOOKED OUT R WINDOW AND SAW A CHEROKEE HEADING RIGHT FOR US; SAME ALT; AND ABOUT 50 FT AWAY. BEFORE I COULD GRAB THE YOKE AND PUSH; THE CHEROKEE VEERED SHARPLY L AND CROSSED BEHIND OUR TAIL. I CALLED TWR AND SAID; 'TWR; WE JUST HAD A CLOSE ENCOUNTER UP HERE!' THE TWR THEN SHOUTED AT THE CHEROKEE TWICE; 'CHEROKEE; I TOLD YOU TO ENTER THE PATTERN BEHIND THE MOONEY. I TOLD YOU TO ENTER THE PATTERN BEHIND THE MOONEY!' I DON'T THINK THERE WERE ANY OTHER PLANES IN THE PATTERN; BUT THERE COULD HAVE BEEN ONE OTHER ON A LONG FINAL. PREVENTION: TWR COULD HAVE AND SHOULD HAVE BEEN MORE VIGILANT IN LOOKING FOR THE CHEROKEE. CHEROKEE PLT SHOULD HAVE FOUND MOONEY (THAT HAD ANNOUNCED MIDFIELD R DOWNWIND) IN THE PATTERN AND ENTERED PATTERN ON XWIND; NOT MIDFIELD. A SLIGHTLY HIGHER ALT ON THE PART OF THE CHEROKEE WOULD HAVE HELPED ALSO.