# A circle whose center is at (1,-3) passes through (7, 5). What is the length of the radius of the circle?

Dec 16, 2016

Radius: $\textcolor{g r e e n}{10}$

#### Explanation:

The radius is the distance from the center to any point on the circumference.

In this case (using the Pythagorean Theorem)
$\textcolor{w h i t e}{\text{XXX}} r = \sqrt{{\left(7 - 1\right)}^{2} + {\left(5 - \left(- 3\right)\right)}^{2}}$

$\textcolor{w h i t e}{\text{XXXX}} = \sqrt{36 + 64}$

$\textcolor{w h i t e}{\text{XXXX}} = 10$