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I have 2 points with their latitude/longitude coordinates and I know that they are in a X miles radius circle (let's say 10 miles radius) somewhere on earth where it's populated (I mean not near the north pole ;) ). I would like to know if these points are very very close of each other or not. When I say very very close, I mean a few meters (let's say 30 meters).

I don't want to use the heavy formula that returns the exact distance between 2 points anywhere on earth. I'm looking for a simplified formula that would simply answer yes or no to the previous question.

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The north/south distance is 1 nautical mile per minute of latitude. The east/west distance is $\cos \phi$ nautical mile per minute of longitude. So you have the total distance in nautical miles is $\sqrt{\Delta \phi^2+\cos^2 \phi \Delta \lambda}$ where the distance is in nautical miles and the angles are in minutes. Alternately, you can express it as $R\sqrt{\Delta \phi^2+\cos^2 \phi \Delta \lambda}, R$ the radius of the earth in your favorite units and angles in radians.

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You could approximate pretty easily by assuming that the surface of the earth is essentially flat within your region. Then, just use the basic euclidian metric (sticking with your longitude and latitude coordinates). i.e. if $\sqrt{(x_1-y_1)^2+(x_2-y_2)^2} for whatever distance $d$ then the points are within d of each other. The only cavet is that you'll require a relatively high degree of precision in your coordinates (though that's obvious if you want to measure distances in meteres). You'll over estimate a bit, but the error should be small as long as the points are close to each other.