Intersection of 2 Rays

Does anyone have code that will determine the geographic location at which 2
rays (lat/lon and direction) will intersect? I could solve this problem
easily by applying a standard Cartesian algorithm, but it seems that it
would introduce possibly HUGE errors as you move further away from the
equator.

If not, can someone more well-versed in the "Great Circle" than I am answer
this question: Can I use lat/lon values in a Cartesian algorithm if my
"rays" don't exceed 2 - 5 kilometers in length? How big would the errors be
on segments of that size?

Any help would be appreciated.

Karl...

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