C172 PLT AND A CESSNA HAD AN NMAC IN HEF CLASS D; AND DC ADIZ.

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I WAS ON R BASE ON A VISUAL APCH TO RWY 16R AT MANASSAS (HEF) I WAS SQUAWKING A DISCRETE CODE IN DC ADIZ ON AN IFR FLT PLAN TALKING TO HEF TWR. OTHER CESSNA WAS CLBING TO MY 2 O'CLOCK POS AND I DSNDED FAST AVOIDING A COLLISION. I FIGURE THE OTHER PLANE HAD JUST DEPARTED RWY 16R AND WAS TALKING TO POTOMAC DEP. ALL PLANES LEAVING HEF NOW HAVE TO USE THE ARSENAL 1 DEP SO I COULDN'T IMAGINE HOW THE PLANE WAS WHERE I WAS. I CALLED TWR AND SAID 'I JUST MISSED THAT PLANE BY 25 FT!' AND THE CTLR SAID 'I HAVE NO IDEA WHO THAT WAS.' AFTER I LANDED I CALLED TWR AGAIN AND ASKED INCREDULOUSLY; 'YOU DIDN'T KNOW WHO THAT OTHER PLANE WAS; THAT THERE WAS ANOTHER PLANE THERE?' AND THE CTLR REPLIED 'NOPE. BUT I'M SORRY THAT HAPPENED TO YOU.' WHAT I WONDER IS HOW; WITH ALL THIS SECURITY AND ALL THESE LAYERS OF CTL AND ALL OF US IN RADAR CONTACT SQUAWKING DISCRETE XPONDER CODES IN THE DC ADIZ; 2 PLANES COULD COME CLOSE TO COLLIDING AND ONE OF THEM WAS NOT EVEN NOTICED BY THE TWR; AND A LONG WAY AWAY FROM ARSENAL 1 AND DEP CTL WAS NOT KEEPING US APART.