Consider the equation of circles as, x2+y2−16x−20y+164=r2 i.e. (x−8)2+(y−10)2=r2 . . . (i) and (x−4)2+(y−7)2=36 . . . (ii) Both the circles intersect each other at two distinct points. Distance between centres =√(8−4)2+(10−7)2=5 ∴|r−6|<5<|r+6| . . . (iii) ∴ If |r−6|<5⇒r∈(1,11) . . . (iv) and |r+6|>5⇒r∈(−∞,−11)∪(−1,∞) From (iii) and (iv), r∈(1,11)