A C172 PLT; ENTERING THE PATTERN AT FXE AS INSTRUCTED BY ATC; HAD AN NMAC WITH A STUDENT PLT OF ANOTHER ACFT.

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ATC CONFIRMED 2 MI N ENTRY TO RWY 8. I RADIOED WHEN ENTERING POS AND WAS INFORMED BY ATC THAT ATC WOULD CALL MY BASE. I READ BACK ATC INSTRUCTIONS; FLYING THE DOWNWIND LEG FOR RWY 8. ATC CALLED MY BASE; AND TOLD ME TO KEEP MY TURNS SQUARE AND TIGHT. I SAW NO TFC IN THE AREA AND WAS NOT INFORMED OF TFC; BUT AFTER TURNING DIRECTLY TO BASE AT 1000 FT MSL/AGL; A CESSNA IMMEDIATELY CAME INTO VIEW IN MY WINDSHIELD; XING THROUGH FROM W TO E. ATC TOLD ME TO TURN L TO AVOID THE PLANE I CUT OFF. I DID NOT RESPOND AS I TURNED THE PLANE; BANKING HARD R TO AVOID THE OTHER ACFT. I RADIOED TO ATC WHAT I DID AND THAT THEY NEED TO CALL OUT THE OTHER ACFT AND A L TURN AS DIRECTED WOULD HAVE CRASHED BOTH PLANES. I PROCEEDED TO LAND AND TELEPHONE THE FXE SUPVR; WHO CALLED ME BACK AFTER LISTENING TO THE TAPES AND RADAR. HE SAID HE TOOK THE CTLR OFF DUTY TO LET HIM 'COOL DOWN' AND HE WAS SORRY FOR THE POOR SVC. I WAS INFORMED THE OTHER PLT WAS A STUDENT WHO HAD COST HIM 2 GAR'S OF OTHER ACFT THAT DAY DUE TO THEIR (THE OTHER ACFT) TERRIBLE FLT CTL -- WHICH I WOULD ATTEST TO AS WE FOLLOWED THEM ON FINAL. THE OTHER PLANE WAS ALL OVER THE GS.