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As air tries to rush in to fill up the low pressure region, Coriolis force deflects it to the right.  It starts to circulate counterclockwise.
A better way to think about circulation at mid latitudes
The more the air tries to rush in to the low pressure area, the faster it circulates.
This is like a gyroscope – which moves at right angles to the way you try to turn it.
Now think of this as view looking down on a low pressure region