C182 PLT ON APCH TO KOA ARPT HAS COM CONFUSION REGARDING POS AND NMAC WITH A BONANZA AT 2 MI. ATC DOES NOT SEEM TO BE AWARE OF RPTR POS WHICH MAY HAVE BEEN BASED ON VOR DISTANCES VERSUS ARPT DISTANCE.

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AT 17 NM N OF KOA; I CONTACTED KOA TWR; GAVE POS; KOA TOLD ME TO CONTACT AT 5 NM. AT 8 DME; ARPT WAS APCHING; CONTACTED KOA. KOA TOLD ME TO CONTACT AT 5 MI. AT 5 DME; NEARLY ABEAM ARPT; CONTACTED TWR. TWR TOLD ME TO CONTINUE ALONG ROAD TO 2 MI. AT 2 DME CONTACTED TWR; AS A BONANZA ZOOMED BY AT NEAR ALT TO ME ON APCH TO KOA. TWR ASKED ME IF I COULD SEE THE ARPT BECAUSE COULDN'T SEE ME. I SAID I SEE ARPT AND HAVE OVERFLOWN IT PER TWR INSTRUCTIONS. TWR THINKS I'M AT WRONG ARPT. I SAY I'M LOOKING AT RWY 35. ANOTHER ACFT SEES ME AND REQUESTS TO DO A 360 DEG TURN. THEN I'M GIVEN INSTRUCTIONS TO APCH DOWNWIND RWY 17 FOR LNDG. AS I'M FLYING DOWNWIND; TWR ASKS ME IF THERE'S ANYONE ELSE IN MY AIRPLANE. (MY IMPRESSION IS HE WANTS TO TALK TO MY CFI.) I INFORM TWR I'M CARRYING A PAX BUT I'M THE PIC. I THEN LAND -- NO FURTHER INCIDENT. WHAT DID I DO WRONG? I GAVE RELATIVE BEARING POS RPTS WHICH LED TO A RELATIVE CONFUSION. NEXT TIME I WILL SUPPORT MY POS RPTS WITH LANDMARK REFS. ALSO; I RELIED ON DME/VOR BUT IT IS OFFSET FROM ARPT BY 4 MI OR SO. I ALSO ASSUMED THAT THE TWR KNEW WHERE I WAS AND WAS TAKING ME TO RWY 35 ON PURPOSE. NEXT TIME I'M GOING TO ASK THE TWR; 'DO YOU SEE ME BECAUSE I SEE YOU!'