Given, equation of circle x2+y2+4x+16y−30=0 ...(i) Comparing with x2+y2+2g1x+2f1y+c1=0 We have, g1=2,f1=8,c1=−30 Let equation of circle whose centre at (1,2) is x2+y2−2x−4y+c=0 ...(ii) Here, g2=−1,f2=−2,c2=c Circles Eqs. (i) and (ii) are orthogonal, then 2(g1g2+f1f2)=c1+c2 ⇒2(−2−16)=−30+c or c=−6 From Eqs. (ii), we get x2+y2−2x−4y−6=0 Radius =√(−1)2+(−2)2−(−6)=√11