I am currently working on a riddle. I have to search and locate a person, but I do not know, where he is. I only have some informations, concerning the probability where he might be.
A satellite offers the following information: with 95% probability the person is located within 1200m distance of the satellite’s path (assuming a normal probability distribution). And it is further known that the Satellite path is a great circle path between coordinates
40.638642, -73.949676
40.626591, -73.935857
EDIT: I edited the title and the post, since the comment showed me that the actual problem for me is the term "great circle". So how do I have to understand this puzzle refereing to great circle?
Like this?
And how should I solve the puzzle? What I am not gettint is what this is aiming at. So the great circle is around the complete earth? Then my scatch is wrong, because I only connected both points? So it is meant that the path is described by those two points and the satelitte itself is cycling around the world, where his path can be described by these two points? Mh, I am baffled....
I believe you are a bit off course…
Your quoted text speaks about a great circle, which is a geodesic of a sphere. So on the sphere, the shortest connection between two points along the surface is a great circle arc, not a straight line in space. Think about e.g. the equator of the eath. In your map this could well be approximated by a straight line, although if the points were further away, then you might have to take curvature and map projection into account. Drawing a simple planar circle in the map you depicted is certainly not what the term great circle refers to.
In a second step, you'd take offset curves at an offset of 1200m on either side of that path. On the sphere, these would be circles but not great circles. Think about parallels in the geographic term, which are offset curves to the equator. But in your map, if you approximate the great circle path by a straight line, then these would simply be parallel lines.
To explicitely answer your question about the center and radius of the circle: its center would be the center of the earth, and its radius would be the radius of the earth. That's pretty much the definition of a great circle.
Since you now ask about intuition regarding these circles, here is an illustration:
The blue circle is a great circle. Its center is the center of the sphere, and its radius is the radius of the sphere. The red circles are offset curves. They have the same distance from the blue curve, but are not great circles. Of course, in this case the red curves would be far more than 1200m away from the blue one, at least if the sphere were really the earth.