Circles SAT question

The correct answer is $5$. The standard form of an equation of a circle in the xy-plane is ${(x-h)}^2+{(y-k)}^2=r^2$, where $h$, $k$, and $r$ are constants, the coordinates of the center of the circle are $(h,k)$, and the length of the radius of the circle is $r$. It′s given that an equation of the circle is ${(x-2)}^2+{(y-9)}^2=r^2$. Therefore, the center of this circle is $(2,9)$. It’s given that the endpoints of a diameter of the circle are $(2,4)$ and $(2,14)$. The length of the radius is the distance from the center of the circle to an endpoint of a diameter of the circle, which can be found using the distance formula, $\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$. Substituting the center of the circle $(2,9)$ and one endpoint of the diameter $(2,4)$ in this formula gives a distance of $\sqrt{{(2-2)}^2+{(9-4)}^2}$, or $\sqrt{0^2+5^2}$, which is equivalent to $5$. Since the distance from the center of the circle to an endpoint of a diameter is $5$, the value of $r$ is $5$.