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On a map, a closed shape defined by a connected sequence of x,y coordinate pairs, where the first and last coordinate pair are the same and all other pairs are unique.

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Get all points with in some range of a point (or range of point) in MySQL

I'm not to familiar with the MySQL spatial functions but from a quick look at the docs you should be able to to buffer your original points by 10m to create a new geometries and then use the st_within …
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