There is a small but still a difference between "included in the radius" and "is square". Square the decision easier for him to do serious GIS artillery is not needed, and is lightning fast.
0. Assume that the coordinates of the point in radians you have stored in the database, the fields lat and lng.
1. Create one index on both fields to speed up queries.
2. In the code translate 10 km in radians (I think, one meter 0,1988 radian, but check).
3. To determine which points are in a square with sides 10 km from a given point in the center, write the following query:
SET @lat = 51.526613503445766; # given in the statement SET @lng = 46.02093849218558; SET @half= [10 km in radians] / 2 ; SELECT id FROM points WHERE lat BETWEEN @lat - @half AND @lat + @half AND lng BETWEEN @lng @half AND @lng + @half;
The first 3 lines (SET) it is necessary to remove and replace them in the query to use the variables from your language of application server (Python, as I understand it).
If you need an exact value (because the earth is not a smooth ball) or radius, see the decisions other authors.