How to calculate distance from a point to a line segment, on a sphere?

Question

I have a line segment (great circle part) on earth. The line segment is defined by the coordinates of its ends. Obviously, two points define two line segments, so assume I a

Answer 1

For distance up to a few thousands meters I would simplify the issue from sphere to plane. Then, the issue is pretty simply as a easy triangle calculation can be used:

We have points A and B and look for a distance X to line AB. Then:

Location a;
Location b;
Location x;

double ax = a.distanceTo(x);
double alfa = (Math.abs(a.bearingTo(b) - a.bearingTo(x))) / 180
            * Math.PI;
double distance = Math.sin(alfa) * ax;