Geo_shape query: LineString: Intersects

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I need to check if my linestring or part of my linestring falls within or intersects my circle with a given radius.

Mapping: Its a lineString type with two coordinates (start and end). Say a long road,

"geometry": {
                        "type": "geo_shape",
                        "tree": "quadtree"
                    }

I have a lat,lon and a radius.

Query: I need to check whether this lineString lies within or intersects my circle.
Further Query: I have many such lineStrings and need to get it sorted from the nearest line.

Can anyone please help me here ?

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