Given, equation of circle is x2+y2−2x−2y+1=0 Centre of circle =(1,1) and radius =1 unit The point B lies on the circle, the coordinate of B is (1+cos‌θ,1+sin‌θ). Given, coordinate of A is (0,−2) (AB)2=(1+cos‌θ)2+(1+sin‌θ+2)2 ‌=1+cos2θ+2‌cos‌θ+9+sin‌2θ+6sin‌θ ‌=11+2‌cos‌θ+6sin‌θ As we know that −√a2+b2≤a‌cos‌θ+bsin‌θ≤√a2+b2 So, −√4+36≤2‌cos‌θ+6sin‌θ≤√4+36 −2√10<2‌cos‌θ+6sin‌θ≤2√10 Maximum value of (AB)2 is 11+2√10.