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(to simplify calculations, I assume a spherical earth. All distances are assumed measured "as the crow flies")

Suppose we have the lon/lat coordinates for two points (p_1,p_2) less than Nkm apart.

Then, around point p_1 I draw a circular polygon c_1 of the set of all points at distance exactly Nkm from p_1 and likewise for p_2 and c_2.

Now c_1 and c_2 will cross at two points. Is there a formula to find the coordinates of these two crossings? If such a thing exists, a pointer to an R/python code doing this would be just as good as a formula.

marked as duplicate by Community Mar 11 '16 at 10:11

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