PA44 INSTRUCTOR AND STUDENT AND A C400 SERIES CESSNA HAD AN NMAC IN VGT CLASS D AIRSPACE.

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CALLED VGT TWR 10 MI NW OF ARPT; RETURNING FROM PRACTICE AREA. INSTRUCTED TO PROCEED STRAIGHT-IN RWY 12R. INSTRUCTION REPEATED BACK TO TWR. TWR TOLD ANOTHER ACFT TO 'CANCEL ALT RESTR.' OUR ACFT WAS NEVER INFORMED OF THE OTHER ACFT INBOUND. ON 2 MI FINAL WE HAD NOT YET RECEIVED A LNDG CLRNC. I INQUIRED WITH THE TWR IF WE WERE CLRED TO LAND. TWR DID NOT RESPOND TO US; BUT INSTEAD TOLD THE TWIN CESSNA THAT HE WAS CUTTING OFF A SEMINOLE (OUR ACFT) ON FINAL. I KNEW HE WAS REFERRING TO US; LOOKED TO THE R AND SAW THE OTHER TWIN TURNING BASE TO FINAL AND APPROX 700 FT. I GRABBED THE CTLS FROM THE STUDENT. SAW THE OTHER ACFT MAKE A CLBING L TURN SO I DOVE L TO AVOID. SEVERAL SECONDS AFTER THE INCIDENT; TWR ADVISED US OF 'TFC ALERT; TAKE ANY ACTION NECESSARY.' I ADVISED TWR THAT WE MISSED; THE OTHER ACFT WAS BEHIND; AND ASKED IF WE WERE CLRED TO LAND. TWR THEN CLRED US TO LAND RWY 12R. WE LANDED WITHOUT FURTHER INCIDENT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: IN CONTACT WITH LAS TRACON; IT WAS DETERMINED THE VGT TWR IS EQUIPPED WITH A BRITE RADAR. QUALITY ASSURANCE WAS AT A LOSS AS TO WHY THE ATCT LCL CTLR DID NOT USE THIS RADAR TO ASSIST HIS CTL OF TFC.