Get an automatic centre punch.
Keep the punch straight and punch a dot as close as you can to the circumference of the bolt.
Punch in the same place four or five times to deepen the dot.
Then place the punch in the dot, but keep it tangential to the circumference.
Punch tangentially and you'll be able to rotate the broken bolt.
I've extracted a number of broken bolts using this method.
Get an automatic centre punch.
Keep the punch straight and punch a dot as close as you can to the circumference of the bolt.
Punch in the same place four or five times to deepen the dot.
Then place the punch in the dot, but keep it tangential to the circumference.
Punch tangentially and you'll be able to rotate the broken bolt.
I've extracted a number of broken bolts using this method.