[blucar]

What I am going to suggest to remove a broken bolt might sound crazy, but it works.
Use a small gas welder with a small tip, 0 or 00, set the gas for a neutral flame, put on safety glasses, face shield and leather welding cape.
Put the flame on the broken bolt, as the bolt heats up and starts to turn cherry red, keep the flame on the bolt, just as the bolt turns molten it will explode out of the hole.
The hole will be quiet clean with small amounts of slag. After cooling run a drill bit down the hole, then clean the treads with the correct size tap.
I have used the above method to remove broken manifold bolts from an engine on two occasions.