Question

what is the radius of this circle?

Explanation:

Step1: Locate center and a point on circle

The center of the circle is at $(4,0)$ and a point on the circle is $(0,4)$.

Step2: Use distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 4,y_1 = 0,x_2=0,y_2 = 4$. So $d=\sqrt{(0 - 4)^2+(4 - 0)^2}=\sqrt{(- 4)^2+4^2}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}$.

Answer:

$4\sqrt{2}$