If the circles x 2 + y 2 - 16 x - 20 y + 164 = r 2   and ( x - 4 ) 2 + y - 7 2 = 36 intersect at two distinct points, then:

Step-by-step solution

As we know, if two circles intersect each other, then r 1 - r 2 < C 1 C 2 < r 1 + r 2 ........(i) Now for the first circle C 1 8 ,   10 and r 1 = r For the second circle C 2 4 ,   7 and r 2 = 6 From (i) r - 6 < 5 < r + 6 ⇒ r - 6 < 5         . . . ii & 5 < r + 6       . . . iii r - 6 = r - 6 ,   r ≥ 6 6 - r ,   r < 6 from iii r > - 1       . . . iv from ii when - 1 < r < 6 then 6 - r < 5 &#86