NDA Math Circle

Given equation o f circles
(x−1)2+(y−3)2=r2
(h1,k1)≡ coordinates of centre≡(1,3)
∴x2+y2−8x+2y+8=0
⇒(x−4)2+(y+1)2=(3)2
(h2,k2)≡coordinates o f centre≡(4,−1)
Radius of circle one =r1=r
Radius of circle two =r2=3
∵ Circle intersects at two points so distance between circle is d<r1+r2
5<r+3
r>2