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The cyclist leans to one side while going along a curve. He leans to wards the curve or center of curvature of the curve.  He avoids skidding and falling by bending.

He does it in order to supply centripetal acceleration. It is necessary to make the cycle turn. If he does not bend, he will move only in a straight line and go away to outside of the curved road. 

The resultant force of the normal force from the road and the friction force supplies the centripetal force required to turn in a curve.

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