Given circles are ‌(x−1)2+(y−3)2=r2 ‌ and ‌‌x2+y2−8x+2y+8=0 For circle (i), C1=(1,3),r1=r For circle (ii) C2=(4,−1),r2=√16+1−8=3 Since, both the circles intersect in two distinct points, therefore ‌r1−r2<C1C2<r1+r2 ⇒r−3<√9+16<r+3 ⇒r−3<5<r+3 ⇒r<8‌ and ‌2<r ⇒2<r<8