# Computing circle and line intersection given in terms of longitude and latitude

Suppose i have a circle whose mid point is given by $$(X,Y)$$ where $$X$$ and $$Y$$ represent longitude and latitude. The radius of the circle is 1 KM.

Now If i have line given by $$(X_1,Y_1)$$ and $$(X_2,Y_2)$$ where $$X_1$$,$$Y_1$$ represents begin longitude,latitude and $$X_2$$,$$Y_2$$ represent final longitude and latitude.

How can i compute if the line intersects the circle? Radius of the circle is in KM.

• You tagged this with map-projections. Is a projection involved? From what to what? Are latitude and longitude measured on the Earth? Do you care that the Earth is not exactly spherical, or is a spherical approximation good enough? Are the circle and line defined as a circle and line on the projection or on the original surface of the Earth? What kind of "line" is the "line"--a great circle arc, a rhumb line, something else? Perhaps it would be better if you edit the question to tell us everything you know about this problem--exactly where it came from and how it was presented. – David K Jun 9 at 21:54