Question

Which of the following points lies on the circle whose center is at the origin and whose radius is 13?

Answer 1

any point that is on the circle will  have a distance of "radius" units, namely 13 units, since the radius is just that.

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ \stackrel{origin}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})}\qquad (\stackrel{x_2}{-5}~,~\stackrel{y_2}{12})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(-5-0)^2+(12-0)^2}\implies d=\sqrt{(-5)^2+12^2} \\\\\\ d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13$