A key snapping in the lock is one of the most common calls we get — and one of the easiest to make worse. Here's how to handle it calmly.
Don't push the broken end further in, and don't insert the other half to "turn it out" — that jams the two pieces together and can damage the cylinder for good. If the door is open, don't lock it again until the fragment is out.

Superglue on the other half (it welds the fragment inside), drilling blind (you'll destroy a repairable cylinder), or forcing anything with brute strength. These turn a €130 extraction into a €390 lock replacement.

If the fragment is flush or below the lock face, or the key turned as it broke, call — we extract the piece with the right tool, test the mechanism, and only replace the cylinder if it's genuinely damaged. Price announced before we come.
One call in English — a fixed price — a technician at your door in ~30 minutes.