Drawing Triangles from a List of Incircles?

Question

I have drawn the incircles of triangles which were generated through a delaunay triangulation but lost the original delaunay mesh. Is it possible to invert the process and draw the triangles back from this list of circles?

Many thanks,

Arthur

Answer 1

If there is a way to find a line mutually tangent to a pair of circles, then drawing tangents to pairs of neighbouring circles would produce the mesh.

If the circles X and Y have radii of x and y and a distance between them of z then, because the radii meeting the tangent are parallel, the angles between the radii and the line connecting the centres of the circles are equal, and given by cos((x+y)/z).