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considering the line of centres to be the x- axis, & the distance between the centres as 2t c1=(t,0) c2=(-t,0) s1=(x-t)2+y2=r2 s2=(x+t)2+y2=R2 now s1/r +/- s2/R=0 implies Rs1+/-rs2=0 Rs1+rs2=0 becomes x2+y2-2t(R-r/R+r)x+t2-rR=0.......[1] Rs1-rs2=o becomes x2+y2-2t(R+r/R-r)x+t2+rR=0......[2] from [1]&[2], 2g1g2+2f1f2=2[-t(R-r)/R+r][-t(R+r)/R-r]=2t2=(t2-Rr)+(t2+Rr)=c1+c2 2g1g2+2f1f2=c1+c2 implies the 2 circles are orthogonal
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