TS EAMCET 11-Sep-2020 Shift 1 Solved Paper

Let equation of circle touches the positive coordinate axes having radius r is
(x−r)2+(y−r)2=r2...(i)
∵ The circle (i) touches the another given circle x2+y2−12x−10y+52=0 externally then
c1c2=r1+r2
Where c1(r,r),c2(6,5),r1=r and r2=3
∴‌‌√(r−6)2+(r−5)2=r+3
⇒‌‌2r2−22r+61=r2+6r+9
⇒‌‌r=2 or 26
∴ There are two possible circles having centres (2,2) and (26,26) respectively.
So, required distance between centres
=5 or 29.