If two circles `(x-1)^2+(y-3)^2=r^2` and `x^2+y^2-8x+2y+8=0` intersect in two distinct points then
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We have circle`(x-1)^(2)+(y-3)^(2)=r^(2)` having centre `C_(1)(1,3)` and radius `r_(1)=r` and circle `x^(2)+^(2)-8x+2y+8=0` having centre `C_(2)(4,-1)` and `r_(2)=sqrt(4^(2)+(-1)^(2)-8)=3`. Circles intersect in two distinct points if `|r_(1)-r_(2)|ltC_(1)C_(2)ltr_(1)+r_(2)` `:. |r-3| lt 5ltr+3` `implies |r-3| lt5` and `rgt2` `implies -5 lt r-3lt5` and `rgt2` `implies -2 lt rlt8` and `rgt2` `implies 2ltrlt8`
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