How can I find all nodes around a point that are members of a way with a certain tag?

I would like to find all highway way member nodes in a certain radius. I cannot see how to do this without using intersection, however, that is not in the API. For example I have this:

[out:json];
way(around:25, 50.61193,-4.68711)["highway"];>->.a; 
(node(around:25, 50.61193,-4.68711) - .a);
out;

Result set .a contains the nodes I want but also nodes outside the radius - potentially a large number if the ways are long. I can find all the nodes inside the radius I don't need, as returned by the complete query above. Now I can always perform a second around query and do the intersection of the two result sets outside of Overpass. Or I can do another difference:

[out:json];
way(around:25, 50.61193,-4.68711)["highway"];>->.a; 
(node(around:25, 50.61193,-4.68711) - .a)->.b;
(node(around:25, 50.61193,-4.68711) - .b);
out;

This gives the result I want but can it be simplified? I'm certain I'm missing something here.

Solution

Indeed, your query can be simplified to an extent that we don't need any difference operator at all. I would recommend the following approach:

We first query for all nodes around a certain lat/lon position and a given radius.
Based on this set of nodes we determine all ways, which contain some of the previously found nodes (-> Hint: that's why we don't need any kind of intersection or difference!).
Using our set of highway ways we now look again for all nodes of those ways within a certain radius of our lat/lon position.

In Overpass QL this reads like:

[out:json];
node(around:25, 50.61193,-4.68711);
way(bn)[highway];
node(w)(around:25, 50.61193,-4.68711);
out;

Try it on Overpass Turbo