My doorbell rings as long as somebody pushes the button. I measured 10V AC at the bell when it is ringing. Now I would like to use this AC voltage to switch another circuit. How can I achieve this?

Here is what I want to happen when the doorbell button is pressed:

1. Let the doorbell ring. That is currently the case.
2. Close another circuit, which is independent from the first one.

Edit: As Olin says in a command, the proposed duplicate is about how to get the doorbell signal into a arduino and not about closing another circuit.