Rosette of lines through a centre

I want to make a compass rose, with a number of straight lines at equally spaced angles going through a common centre, like this:

I’ve tried drawing one line and then rotating it by 10 degrees repeatedly, but the line drifts off-centre, presumably because of rounding errors in the repeated arithmetic. Is there a better way?

I’m quite sure this is not a rounding problem. Possibly you use command-v to paste copies. This will not paste on top of the original but with a small offset (or at the position where you clicked after the copy and before the paste). Try using shift-command-v to “paste in place”.

Perfect. Thanks t_j