# A circle has center (1,3) and passes through (4,-1) How do you use the distance formula to find the length of the radius of the circle?

Apr 5, 2016

By definition the radius of a circle is the distance between the center and any point on the circumference of the circle.

#### Explanation:

If a circle has
$\textcolor{w h i t e}{\text{XXX}}$center at $\left(1 , 3\right)$
and
$\textcolor{w h i t e}{\text{XXX}} \left(4 , 1\right)$ is a point on the circumference.

The radius of the circle is
$\textcolor{w h i t e}{\text{XXxX}} r = \sqrt{{\left(1 - 4\right)}^{2} + {\left(3 - 1\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXxX}} = \sqrt{{3}^{2} + {2}^{2}}$

$\textcolor{w h i t e}{\text{XXxX}} = \sqrt{13}$