i want a example of ths question because i dont understand properly ….......f c1(x1,y1),c2(x2,y2) then point of contact is given by (r1x2+r2x1 by r1+r2 , r1y2-r2y1 by r1+r2)

when we draw tangents to two circles the line joining point of contacts to the centres of these two circles divides the line in the ratio of r1:r2 externally and internally for transverse & direct common tangents respectively for an example-
https://www.askiitians.com/iit-jee-coordinate-geometry/common-tangents.aspx