HIGH MINIMUMS CAPT MISSES APCH WHEN CEILING AT MISSED APCH POINT IS LOWER THEN RPTED.

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PERFORMING LOA/DME 19 APCH TO REAGAN NATIONAL. WE USED CAT D MINIMUMS OF 720 FT MDA; 2 1/4 MI VISIBILITY. I AM A HIGH MINIMUMS CAPT; THUS; WE ADD 100 FT TO THE MDA AND 1/2 MI VISIBILITY. WX WAS ADVERTISED AS 1000 FT CEILING; 3 MI VISIBILITY. AT THE MISSED APCH POINT; THE CLOUDS WERE LOWER THAN RPTED; NEVER SAW THE RWY. SO; WE EXECUTED THE MISSED APCH. I CALLED MISSED APCH TO TWR (FREQ WAS SOMEWHAT BUSY). THE LCL CTLR; SOUNDING SOMEWHAT SURPRISED; ASKED IF WE WERE GOING AROUND. I REPLIED 'YES.' NEXT TWR XMISSION WAS AN INSTRUCTION FOR AN IMMEDIATE 120 DEG HDG ALONG WITH 'TFC LESS THAN A MI.' DURING THE GAR; I WAS DISTR BY AN INCREASE IN AIRSPD. THE AIRPLANE WAS PERFORMING BETTER THAN I EXPECTED. I THEN NOTICED THAT WE WERE CLBING THROUGH 2000-2100 FT. I BRIEFLY TOOK CTL OF THE AIRPLANE TO STOP THE CLB WHILE SIMULTANEOUSLY RECEIVING AN INSTRUCTION FROM TWR TO 'TURN TO 120 DEG HDG; MAINTAIN 3000 FT.' THE FO; DURING THE GAR; DID SEE THE CONFLICTING TFC THROUGH THE BREAKS IN THE CLOUDS (HE WAS BELOW US; ALT UNKNOWN); HOWEVER; NO TCASII ALERT WAS EVER RECEIVED. IT IS BELIEVED THAT THE TFC DEPARTED DCA ARPT ON A SOUTHERLY COURSE. THIS CONCERNED US; BECAUSE IT SEEMED THIS TFC WAS INTRUDING ON OUR MISSED APCH COURSE.