People who work with radiation must be protected, because ionising radiation can damage cells. Workers keep their exposure time short, stay as far from the source as they can, and use tongs to handle sources. They use shielding, such as lead screens and lead aprons, or leave the room while a source is in use. Sources are stored in lead-lined containers. Workers wear badges that record the radiation dose they receive, and these are checked regularly so the dose stays within safe limits.
Patients are exposed to radiation for scans and treatments because the benefit is greater than the risk. To limit the dose for patients, they are given the smallest dose that gives a useful result, and the number of exposures is kept as low as possible.
Medical personnel are at risk in a different way. A patient may have a scan only occasionally, but a radiographer or nurse works with radiation every day. Their exposure builds up over many years, so they are at greater risk than a patient having a single scan. This is why they use shielding, leave the room during x-rays, and keep short exposure times.