Have a closer look at the overpass-api parameter "**around**" ... maybe at [Overpass_API/Overpass_QL][1]
BUT:
How will you differentiate when there are other ways around your position that hou have lat lon from?
And: what is the source of your lat/lon? lat/lon?
Is it sure that each coordinate is a single node wich is an element of a certain way?
Or is your lat/lon only "near" any posible street?
[1]: http://wiki.openstreetmap.org/wiki/Overpass_API/Overpass_QL
Have a closer look at the overpass-api parameter "**around**" ... maybe at [Overpass_API/Overpass_QL][1]
BUT:
How will you differentiate when there are other ways around your position that hou have lat lon from?
And: what is the source of your lat/lon? Is it sure that each coordinate is a single node wich is an element of a certain way?
Or is your lat/lon only "near" any posible street?
[1]: http://wiki.openstreetmap.org/wiki/Overpass_API/Overpass_QL