How to limit query to parts of highways strictly inside an area or use boundary as polygon

I want to perform some analyses on the cycleways in my town. To do this I exported the cycleways using the following overpass query:

[out:json];
area[name="Segrate"];
way["highway"="cycleway"](area);
(._;>;);
out;

I noticed that some of the returned cycleways are outside of the town, which is very clear if you run this query, in which I also draw the town boundaries.

It appears that if the cycleway has a part inside the area and one outside, also the outer part is included in the query response.

• Is there a way to limit the response of the query regarding a area, to the parts of the highways strictly inside that area?
• Alternatively, how can I use the boundaries as a polygon to limit the returned highways at the nodes that are inside?