POTENTIAL CONFLICT ENSUES BTWN A TRANSITING VFR GA ACFT AT 850 FT AGL 2 MI S OF RWY 1 AND A C172 ON FINAL APCH FOR SAME RWY AT FAI; AK.

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I WAS APCHING FAI FROM THE SE; HAD CONTACTED APCH AND HAD BEEN GIVEN A XPONDER CODE. THEY ACKNOWLEDGED RADAR CONTACT. FAI IS A TRSA. I WAS HEADED FOR A SMALL; PVT AIRSTRIP (CHENA MARINA) WHICH IS ABOUT 2 MI W OF FIA. WHEN I WAS ABOUT 5 MI OUT; APCH HANDED ME OVER TO THE TWR. I WAS IN RADIO CONTACT WITH TWR. MY FLT PATH REQUIRED ME TO CROSS THE APCH PATH TO RWY 1L OF FIA AT ABOUT A 90 DEG ANGLE 1-2 MI S OF THE ARPT. RWY 1L WAS ACTIVE. TWR ADVISED ME OF TFC; A C172 ON APCH TO RWY 1L. I SAW THE TFC AND ADVISED THE TWR. I CONTINUED ON THE SAME RTE. AS I CONVERGED WITH THE OTHER AIRPLANE; I COULD SEE THAT I WOULD PASS IN FRONT OF IT; BUT AT A CLOSER PROX THAN I NORMALLY WOULD HAVE BEEN COMFORTABLE WITH. HAD I NOT BEEN SO CLOSE TO FIA; IN A TRSA; IN CONTACT WITH TWR; AND PRESUMABLY IN THEIR SIGHT AND ON THEIR RADAR; I WOULD HAVE MANEUVERED TO REDUCE THE PROX WITH THE OTHER AIRPLANE. BUT I FIGURED THAT'S WHAT TRSA'S ARE ALL ABOUT -- I ASSUMED THEY WOULD HAVE DIRECTED ME OR THE OTHER AIRPLANE TO A RTE THAT PROVIDED GREATER SEPARATION IF THEY THOUGHT IT APPROPRIATE. I PASSED IN FRONT OF THE OTHER AIRPLANE AS ANTICIPATED -- CLOSE; BUT NOT A 'NEAR MISS' IN MY OPINION. MY RECOLLECTION IS THAT THE DISTANCE UPON XING WAS ABOUT 1000 FT (WE WERE AT ABOUT THE SAME ALT). HOWEVER; THE OTHER PLT FREAKED (I DON'T THINK SHE SAW ME UNTIL I WAS IN FRONT OF HER). SHE READ THE RIOT ACT TO THE TWR AND THEY SUBSEQUENTLY CALLED ME AND ASKED THAT I CALL THEM UPON LNDG. WHEN I DISCUSSED THE MATTER WITH THE TWR PERSONNEL; THEY ADVISED THAT; EVEN IN A TRSA; IT WAS STILL MY RESPONSIBILITY TO MAINTAIN ADEQUATE SEPARATION FROM OTHER ACFT. IT SEEMS I HAD AN INCORRECT UNDERSTANDING OF THE LEVEL OF SCRUTINY THE CTLRS MAINTAIN. IN THE FUTURE; I WILL TRUST MY OWN JUDGEMENT OF WHAT'S TOO CLOSE A LITTLE MORE AND RELY A LITTLE LESS ON THE CTLRS TO DIRECT MY RTE SUCH THAT 'ADEQUATE' SEPARATION IS MAINTAINED (EVEN THOUGH I STILL THINK THAT'S WHAT A TRSA IS SUPPOSED TO BE FOR).