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Two circles centres `A and B` radii `r_1 and r_2` respectively. (i) touch each other internally iff `|r_1 - r_2| = AB`. (ii) Intersect each other at two points iff `|r_1 - r_2| ltAB lt r_1+ r_2`. (iii) touch each other externally iff `r_1 + r_2 = AB`. (iv) are separated if `AB gt r_1 + r_2`. Number of common tangents to the two circles in case (i), (ii), (iii) and (iv) are 1, 2, 3 and 4 respectively. If circles `(x-1)^2 + (y-3)^2 = r^2 and x^2 + y^2 - 8x + 2y + 8=0` intersect each other at two different points, then : (A) `1ltrlt5` (B) `5ltrlt8` (C) `2ltrlt8` (D) none of these

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