Question

A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?

Answer 1

Check the picture below.

$\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 0}}\quad ,&{{ 0}})\quad % (c,d) &({{ 5}}\quad ,&{{ -12}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2} \\\\\\ r=\sqrt{(5-0)^2+(-12-0)^2}\implies r=\sqrt{5^2+(-12)^2} \\\\\\ r=\sqrt{25+144}\implies r=\sqrt{169}\implies r=13$