Riding our bikes on city street teaches many things. The all time life-saver is:
If you can, never enter an intersection without another vehicle on your right!
If you have to slow down to let a vehicle catch up with you, or increase speed so that you catch up with another vehicle. Having a vehicle on your right side is as safe as it gets for entering an intersection.
By the way, it is safer that the vehicle be on your right than on the left. The closer you can be to the center of the intersection when you go through it, the more distance there is (on an average) between you and somebody that comes at you from either side. This is just another way of saying that if you have to enter the intersection by yourself, do it in the left-most lane.
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