Let equation of circle be (x−h)2+(y−k)2=52, where 5 is the radius of the circle. Also, the radius of given circle c1:x2+y2−2x−4y−20=0 is given by √1+4+20=5 units
∵ Two circles touch each other externally. ∴(5,5) is the mid-point of line segment joining (h,k) and (1,2) ⇒5=
h+1
2
,5=
k+2
2
⇒h=9,k=8 ∴ Equation of circle becomes(x−9)2+(y−8)2=52