# How do I find the intersections of 2 circles on earths surface?

I have the circles' center in lat & long, as well as the radius in meters. How do I find the circles intersections?

Edit: EXAMPLE:

Circle 1: Center on Earth's surface (43.564627,-116.220524) These values are Latitude and Longitude
Radius: 15 Meters a Length on the surface of the earth

Circle 2:  Center on Earth's surface (43.564736,-116.219741) These values are Latitude and Longitude
Radius: 15 Meters a Length on the surface of the earth


Expressed in Latitude and Longitude, where do these circles intersect?

I am unsure of the best method to find the closest results, accuracy within 2 meters should be alright.

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and presumably also the radius of the Earth? or does that divide out of the answer? –  Mitch May 29 '11 at 19:27
What do you mean the circles' center? Edit for clarity: is a circle on the Earth a set of points on the surface of the earth equidistant from some point, that point being the "center"? –  Kopper May 29 '11 at 19:27
@Jay: What else could it be, given the wording of the question? It's certainly not a Great Circle. –  TonyK May 29 '11 at 20:03
@Seth: A minor technical point: is this radius measured along the surface of the earth, or as a distance in Euclidean 3-space? (Minor, because it doesn't affect the method used to solve the problem.) –  TonyK May 29 '11 at 20:04
@Seth: you have clarified nothing. (i) Surface distance, or 3-space distance? (ii) "The earth's mean equator length"? Come on. –  TonyK May 31 '11 at 19:58