NMAC -- PLT SEES ANOTHER ACFT BTWN HIS ACFT AND THE ARPT; BUT TURNS TOWARD THE OTHER ACFT ANYWAY AND HAS A NEAR HIT.

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IN SLOW CRUISE FLT (APPROX 100 KIAS) SW DIRECTION SECOND ACFT (HIGH-WING CESSNA) IN VISUAL CONTACT ON PARALLEL COURSE TO R OF MY ACFT; SAME ALT; AHEAD OF WING; SIMILAR SPD. I WAS IN CONTACT WITH BKL TWR; OTHER ACFT DID NOT SEEM TO BE ON TWR FREQ (NO XMISSION BEFORE/DURING/AFTER EVENT). ADVISED TWR OF INTENTIONS AND INITIATED 90 DEG TURN TO NW; EXPECTING TO PASS SAFELY BEHIND SECOND ACFT. AT COMPLETION OF TURN; I PASSED BELOW AND BEHIND SECOND ACFT IN CLOSE PROX. UNKNOWN IF SECOND ACFT TOOK EVASIVE ACTION. POSSIBLE CAUSES OF CLOSE PROX TO OTHER ACFT: INACCURATE ESTIMATE OF DISTANCE TO; COURSE OF; AND/OR SPD OF OTHER ACFT AND/OR TURNING RADIUS OF MY ACFT. CHANGE IN COURSE OF OTHER ACFT. CHANGE IN SPD OF OTHER ACFT. CONTRIBUTING FACTORS: LOSS OF VISUAL CONTACT WITH OTHER ACFT. FAILURE TO IMMEDIATELY ABORT TURN ON LOSS OF VISUAL CONTACT WITH OTHER ACFT. OTHER ACFT DID NOT HEAR MY ANNOUNCEMENT OF R TURN. POOR JUDGEMENT: TURNING TOWARD ACFT ON PARALLEL COURSE AT SAME ALT. DELAYING ABORTING OF TURN WHILE TRYING TO REESTABLISH VISUAL CONTACT WITH OTHER ACFT. BETTER CHOICES THAT WOULD HAVE PREVENTED SIT: DSND TO LOWER ALT PRIOR TO TURN WOULD GUARANTEE VERT SEPARATION AND IMPROVE ABILITY TO MAINTAIN VISUAL CONTACT DURING TURN (LOW WING ACFT). SLOW MY ACFT TO INCREASE SEPARATION BEFORE ATTEMPTING TURN. MAKE TURN TO L (270 DEG TURN) AWAY FROM OTHER ACFT. HAVING OTHER ACFT ON TWR FREQ IN CLASS D AIRSPACE WOULD ALSO MAKE HIM AWARE OF MY INTENTIONS.