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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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    @TonyK (i) Surface distance, I have edited my question to include an example, I am very sorry if my lack of understanding is frustrating2011-05-31

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The centres of the circles are separated by 12.120247m North-South and by 63.0874577m East-West so that their separation comes to 64.2411683m. Since each circle has a radius of only 15m, THE CIRCLES DO NOT INTERSECT.