tl;dr: “Am I, with any given location, inside of any number of circles with varying radii”
Assume you have a database full of locations (coordinates) with arbitrary radii. Now the user enters and provides the backend with their current location.
How would the backend efficiently figure out which locations to return?
I’m having a hard time wrapping my head around this and all my googling turns up is the opposite of this (the user location provides the radius and we search for any items in the user circle).
What am I not thinking of? Do I need more coffee?
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More coffee is always good!
As was suggested, there’s almost certainly a geospatial extension for your database, but that may be overkill for what you want. I would base it on squares, rather than circles, and then later refine the selection.

The ‘proper’ method
SELECT * FROM LOCATIONS WHERE ?1 >= X  RADIUS AND ?1 <= X + RADIUS AND ?1 >= Y  RADIUS AND ?1 <= Y + RADIUS

Manhattan distance
SELECT * FROM LOCATIONS WHERE ABS(?1  X) + ABS(?2  Y) <= RADIUS*1.5
The 1.5 (or rather, sqrt(2)) is because this distance is always greater than (or equal to) the true distance.

Store the bounding rectangle rather than the location and radius?
SELECT * FROM LOCATIONS WHERE ?1 >= X_MIN AND ?1 <= X_MAX AND ?2 >= Y_MIN AND ?2 <= Y_MAX
As an added bonus, you could probably create an index on
(X_MIN, X_MAX, Y_MIN, Y_MAX)
and speed things up. 
Create a view for the bounding rectangle if you want to keep location/radius as it is.

Probably lots of other things one can do…
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