Question

what is the radius of this circle?

Explanation:

Step1: Identify circle - center and a point

The circle is centered at the origin $(0,0)$. A point on the circle is $(6,0)$.

Step2: Use distance formula for radius

The distance between the center $(0,0)$ and the point $(6,0)$ on the circle is the radius. 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, $x_1 = 0,y_1 = 0,x_2=6,y_2 = 0$. So $r=\sqrt{(6 - 0)^2+(0 - 0)^2}=\sqrt{6^2}=6$.

Answer:

6