notice the picture, the radius is just the distance from the
center to a point on the circle, thus
[tex]\bf \textit{distance between 2 points}\\ \quad \\\\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{5}}\quad ,&{{ -7}})\quad
% (c,d)
&({{ 8}}\quad ,&{{ -4}})
\end{array}\qquad
% distance value
\\\\\\
\begin{array}{llll}
d = &\sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\\
&\qquad \uparrow \\
&radius
\end{array} [/tex]
[tex]\bf \begin{array}{llll}
d = &\sqrt{({{ 8}}-{{ 5}})^2 + ({{ -4}}-{{(-7)}})^2}\\
&\qquad \uparrow \\
&radius
\end{array}
\\\\\\
d=\sqrt{(3)^2+(-4+7)^2}\implies d=\sqrt{3^2+3^2}\implies d=\sqrt{18}
\\\\\\
d=\sqrt{9\cdot 2}\implies d=\sqrt{3^2\cdot 2}\implies d=3\sqrt{2}[/tex]
