# A circle has a center at (7 ,3 ) and passes through (2 ,7 ). What is the length of an arc covering pi  radians on the circle?

Feb 8, 2016

$\sqrt{41} \pi$

#### Explanation:

If the circle has a center at $\left(7 , 3\right)$ and passes through $\left(2 , 7\right)$
it has a radius of $r = \sqrt{{\left(7 - 2\right)}^{2} + {\left(3 - 7\right)}^{2}} = \sqrt{41}$

The length of an arc covering $\pi$ radians is half the length of the circumference
$\textcolor{w h i t e}{\text{XXX}} \frac{2 \pi r}{2} = \pi r$

So in this case, the length of the arc is
$\textcolor{w h i t e}{\text{XXX}} \pi \sqrt{41}$