Advice on bike routes - from strathfield to north sydney

[nessa42]

Hi,

I am new to Sydney and was wondering whether it was possible
or advisable to cycle from strathfield to
north sydney (australian catholic university,
40 edward street).
I noticed it is about 21 km one way, but that was the car route.
Is biking in Sydney safe (from traffic point of view)
and are they any bike paths that I could take ?

Thanks!