Algorithm: point with N distance of a line between two other points

[japhy]

I have a world map with world events (like volcanoes, earthquakes, hurricanes, etc.) mapped on it. I also have buildings (like the Empire State Building) mapped on it. I can determine through simple math if an event is within N miles of a building. I've done this in Perl and translated the math to a mysql function, since these calculations are done at the database level.

But now I have a more complex sort of "building" to map. This isn't a building in a single place, it's essentially a path, like for a pipeline. The pipeline is defined by its vertices: every place the pipeline changes direction is a vertex (obviously).

I want to determine now if an event is within N miles of this "pipeline". However, this is more than just checking each individual vertex of the pipeline, because it is possible for the event to be too far from a vertex to register a hit, yet close enough to a line drawn between the two vertices (which is the actual pipeline).

I sort of know the math for this situation... I need to test for a point (X0,Y0) on the line from (X1,Y1) to (X2,Y2) -- that's the pipeline -- that is on the perimeter of a circle of radius R from point (X3,Y3) -- that's the event. But I'm not sure I know how to convert that into lat/lng math for use in mysql. Any pointers?