SAT Question b2528e6b: Area and Volume answer and explanation with Desmos solution

It's given that the three points shown define a circle, so the center of that circle is an equal distance from each of the three points. The point $(6,6)$ is halfway between the points $(6,2)$ and $(6,10)$, and is a distance of $4$ units from each of those two points. The point $(6,6)$ is also a distance of $4$ units from $(2,6)$. Because the point $(6,6)$ is the same distance from all three points shown, it must be the center of the circle. Since that distance is $4$, it follows that the radius of the circle is $4$. The circumference of a circle with radius $r$ is equal to $2\pi r$. It follows that the circumference of the given circle is $2\pi (4)$, or $8\pi$. It's given that the circumference of the circle is $k\pi$. Therefore, the value of $k$ is $8$.