Question

if the point (3,-7) is the center of a circle and the point (8,5) is on the circle, what is the circumference of the circle?

Answer 1

find the radius
keeping in mind that \(\bf \textit{circumference}=2\pi r\qquad r=radius\)

Answer 2

so the radius is really the distance between, the center point, and point on the circle
thus \(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ 3}}\quad ,&{\color{blue}{ -7}})\quad
% (c,d)
&({\color{red}{ 8}}\quad ,&{\color{blue}{ 5}})
\end{array}\qquad
% distance value
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\to radius\)