1. **Problem statement:** We are given the center of a circle at point $C(2,1)$ and a point on the circle $P(8,9)$. We need to find: (i) The radius of the circle. (ii) The equation of the circle. 2. **Formula for radius:** The radius $r$ is the distance between the center $C(x_1,y_1)$ and a point on the circle $P(x_2,y_2)$. The distance formula is: $$r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate the radius:** Substitute $x_1=2$, $y_1=1$, $x_2=8$, $y_2=9$: $$r = \sqrt{(8 - 2)^2 + (9 - 1)^2} = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$$ 4. **Equation of the circle:** The general equation of a circle with center $(h,k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 5. **Write the equation:** Using $h=2$, $k=1$, and $r=10$: $$ (x - 2)^2 + (y - 1)^2 = 10^2 $$ $$ (x - 2)^2 + (y - 1)^2 = 100 $$ **Final answers:** (i) Radius $r = 10$ (ii) Equation of the circle: $$(x - 2)^2 + (y - 1)^2 = 100$$