AN ACR B737-200; DEP TFC ON RWY 8 AT HILO HAS CONFLICT WITH A C172 IN DEP CORRIDOR. NMAC OCCURS AS B737 WAS IN THE DEP TURN AT 4100 FT.

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FLT FROM HILO TO HONOLULU. WE WERE CLBING AND TURNING L TO COURSE; WHEN DEP CALLED TFC AT 10 O'CLOCK POS; 4500 FT SBOUND. WE SAID WE WERE LOOKING. DEP CALLED A C172; TELLING HIM OF OUR POS. C172 PLT STATED HE SAW US AND HAD US VISUALLY. WE CONTINUED OUR L TURN CLB TO INTERCEPT HILO 310 DEG RADIAL. WE INITIALLY HAD THE C172 ON TCASII BUT THE TARGET DISAPPEARED DURING THE TURN. AT APPROX 3800 FT THE TARGET 'POPPED-UP' ON TCASII DEPICTED AS YELLOW AND +03. SHORTLY THEREAFTER WE GOT A TA FOLLOWED IMMEDIATELY BY AN RA. I INCREASED TURN AND CLB; CONDUCTING AN EVASIVE MANEUVER UNTIL TCASII INDICATED CLR OF CONFLICT. I NEVER SAW THE C172; THE FO SAW THE C172 AT SAME ALT; APPROX 300 FT; OPPOSITE DIRECTION. THE C172 DID NOT DEVIATE; PASSING OFF THE R SIDE OF THE ACFT. PHONE CALL TO TWR AFTER LNDG; SUPVR STATED NO PROCEDURAL ERROR; RADAR TRACK SHOWED A PREDICTED COURSE SEPARATION OF 1 MI HORIZ; 200 FT VERT. SUPPLEMENTAL INFO FROM ACN 362700: HILO ARPT WAS USING RWY 26 TO LAND AND RWY 8 FOR TKOF. HILO DEP ALLOWED A C172 TO ENTER THE DEP AREA OF RWY 8. HANDED OFF FROM HILO TWR TO DEP AND WAS ADVISED OF TFC AT 12 O'CLOCK. C172 SAID HE HAD US IN SIGHT. WE HAD HIM ON TCASII AND GOT AN RA/TA. HARD L BANK TO AVOID. THAT IS THE TIME OF VISUAL CONTACT AT 3 O'CLOCK AT 300 FT AND SAME ALT. HOW CAN A C172; SEE AND AVOID A B737?