# A circle's center is at (3 ,9 ) and it passes through (5 ,8 ). What is the length of an arc covering (5pi ) /4  radians on the circle?

Aug 7, 2016

$= 8.8$

#### Explanation:

Distance between the points $\left(3 , 9\right)$ and $\left(5 , 8\right)$ is Radius($r$) of the Circle.
Distance or Radius($r$)
=sqrt((5-3)^2+(9-8)^2
$= \sqrt{{\left(2\right)}^{2} + {1}^{2}}$
$= \sqrt{4 + 1}$
$= \sqrt{5}$
$= 2.24$
Circumference of the Circle $= 2 \pi r = 2 \pi \left(2.24\right) = 14.07$
Arc covers $\frac{5 \pi}{4}$ radians of the Circle
or
Arc covers $\frac{5 \pi}{4} \div 2 \pi = \frac{5}{8}$th Circumference of the Circle
Length of the arc $= \frac{5}{8} \left(14.07\right) = 8.8$