# Air corridor in spherical surface: calculating great circle tangent points with small circles

I have the necessity to draw on a sphere (earth) an air corridor.

In the cartesian plane, this corridor is made by some circles and from outer tangents that connect these circles as you can see in this image (central part of the image):

In general circles can have different radii. In flat Cartesian plane I can calculate the two outer tangents (when possible) of two circles, using for example formulas that I can found in this page.

My problem is a bit more complicated. I must to perform same calculus in spherical surface. You can see more clearly in this image:

In this case I've two small circles and I want to calculate tangents between these two circles in spherical surface.

Onto a sphere I don't have straight lines, but geodesics, and in this case they are represented by great circles. I am able to calculate a great circle trajectory between two points using the Aviation formulary.

What I miss is a way to find the small circles tangent points, in order to have the initial and starting points for my geodesic tangents.

How can I calculate them?

• Found a solution for this? – Little Tiny Dev Jun 20 '16 at 11:49
• At the end my team decided to approximate everything considering that they will use small maps, so we draw directly circles on projected plane and use the canonical euclidean way. For them it's sufficient. I've a Mathematica notebook with this problem that I must complete when I will have spare time (never :( ...) – Jepessen Jun 21 '16 at 7:20