Intersection axis of three cones with the same apex

Hello Matlab Community,

I want to create a matlab code that calculates the intersection axis of three cones with the same apex. I have given the coordinates of the apex as well as the centers of the circles base area and the cone angles. However the three cones might not intersect in one axis. Therefore the closest axis to the intersections should be found.

I also thought about calculating the intersections of the base area circles and the axis afterwards but I couldn't find a solution for three circles in 3d space either.

Can you think of an easy way to solve this problem?

Thank you!

Patrick