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Spherical trig application

Given a roughly convex polygon on the Earth's surface - typically 1000
miles "diameter" and 3 - 12 vertices. I need to know whether a given
point is in it or not.  There are about 10,000+ such points to test so
I need an effecient method.

Any ideas, or know of any software that will do something like it.

I guess defining the enclosing circle and discarding any points
outside that would get rid of most of them.

I don't want a lesson in spherical trig, I'm no expert but I know
enough, it's the methods and short cuts I'm after.

Thanks  Roger.

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