# If the two circles $(x-1)^2+(y-3)^2=r^2$ and $x^2+y^2-8x+2y+8=0$ intersect in two distinct point then

$\begin{array}{1 1}(A)\;r >2 \\(B)\;2 < r < 8 \\(C)\;r < 2 \\(D)\;r=2 \end{array}$

$|r_1-r_2| < c_1c_2$ for intersection
=> $r-3 <5 => r <8$ -----(i)
and $r_1+r_2 > c_1c_2$
$r+3 > 5$
=> $r >2$------(ii)
from (i) and (ii) we have $2 < r< 8$
Hence B is the correct answer.