Centre and radii of the given circles are C1(1,3) , r1=r and C2(4,−1),r2=3 respectively. Since, circles intersect in two distinct points, then |r1−r2|<C1C2<r1+r2 ⇒ |r−3|<5<r+3 ..................(i) From last two relations, r>2 From first two relations, |r−3|<5 ⇒ −5<r−3<5 ⇒ −2<r<8 ..................(ii) ∴ From Eq.(i) and Eq.(ii), we get 2<r<8