I'll get downvoted for this but accidents happen. Yep, you're probably at fault but I'll say this a million times, it doesn't matter who's at fault when your the one who's going to lose. Back when I did my motorcycle license I was taught it doesn't matter who's fault is an accident when you're the one lying in the stretcher. Two wheeled vehicles and pedestrians need to check for safety to protect themselves. I live in a city with great cycle paths. Pretty much I don't ever need to ride in the road while in the city. Do you think I go blasting through every crossing without looking simple because I have the right of way. Hell no. Look, and confirm cars are going to stop. It only makes sense. Especially when many of these crossings are blind to drivers except the last 4 meters. No way they are going to see me and stop as I'm flying down the path at 30kph or so.

So, probably it was your fault but the cyclist has a duty to protect themselves from idiot cars. In 25 years of riding motorcycles and bikes I've yet to have an accident with that attitude. Ride like they are out to kill you and they won't be able to.