To find common tangents of two circles, use the centres of similitude. For circles with centres C1, C2 and radii r1, r2: the external centre of similitude E divides C1C2 externally in r1:r2, and the internal centre of similitude I divides it internally in r1:r2. Direct common tangents pass through E. Transverse tangents pass through I. To find the tangent equations: write a line through E (or I) as y-$y_E$=m(x-$x_E$), then apply the tangency condition (distance from C1 to line = r1) to find m. Length of direct tangent = sqrt($d^{2-}$(r1-r2)^2). Length of transverse tangent = sqrt($d^{2-}$(r1+r2)^2). These lengths are the segments between the two tangent points on the respective tangent lines.