Here, C1:x2+y2=r2, centre of circle =(0,0) and radius r1=r And, C2:x2+y2−6x−25=0⇒ x2−6x+9+y2−16−9=0⇒(x−3)2+y2−25=0 ⇒(x−3)2+y2=52 So, centre is (3,0) and radius, r2=5 ∴C1C2=3 Now two circles are intersecting so r1−r2<C1C2<r1+r2 ⇒|r−5|<3<r+5 ⇒r<8 and r+5>3⇒r>2 ∴2<r<8 Hence, option (4) is correct.