Instead, the vet grabbed Hope's broken left horn and it promptly fell off in his hand, leaving a horn bump very reminiscent of Lerris's when he was little, and a small bloody spot towards the front. It turns out that Hope had grown scurs instead of real horns, compliments of her mixed genetics. (Anna is naturally polled.) We checked, and yes, the right horn was also just a scur and not a real horn. With a little work, we got the right horn off without any blood at all.
A scur is a little horn-lette, usually only lightly connected to the skull and lacking in most of the blood vessel/nervous system formation necessary to grow. It will often be stunted, curled, or flat as opposed to round and solid. And, as demonstrated in this case, it will often break or fall off during development. There is a chance that it will regrow, break off, and regrow again (lather rinse repeat), and will require constant monitoring to be sure that there is no infection associated with the breakage.
In order to be shown, Angoras must either have horns or be naturally polled; disbudding is a disqualifying modification. Being that this late-onset of hornlessness* is a case of genetics and not human intervention, Hope is still qualified to show this fall.
*What a whacky concept to have to explain to people!