Erle, the man has a broken tap, not a broken off bolt, if they make some kind of drill bit that will cut a tap, I want to buy one. As already mentioned, sometimes you get lucky and can weld a nut on what's showing, not that taps are considered a weldable alloy, so the choices are, weld a nut on it, a tap removal tool, bust it out with a punch in pieces, or pay a machine shop to blow it out of there with a EDM. Taps are harder than a wedding night you know what, that's why they break so easy, they have no give.