ideas to remove broken fence post?

lots of wing broke one of the 4X4 posts flush with the ground. could have been a low flying cow that smacked it but no way to prove that...and we know pigs don't fly. I've gotten about six inches of old post removed, drilled another 12 inches down the center of that. not sure how deep they go. Thought was drive a metal rod thru the center hole, drill the new post to accept the rod and epoxy the whole she-bang. any ideas? if I knew a family of termites I'd invite them over for a few meals, but they might go elsewhere for dessert. thanks for any and all ideas! Bob
one just came to mind but I don't think a stick of dynamite would be allowed in the area.