# A circle's center is at (2 ,4 ) and it passes through (3 ,1 ). What is the length of an arc covering (15pi ) /8  radians on the circle?

Aug 11, 2016

$= 18.75$

#### Explanation:

Circle's center is at $\left(2 , 4\right)$ and it passes through $\left(3 , 1\right)$
Therefore Length of the $r a \mathrm{di} u s = r$ =Distance between these points$\left(2 , 4\right) \mathmr{and} \left(3 , 1\right)$
or
$r a \mathrm{di} u s = r = \sqrt{{\left(3 - 2\right)}^{2} + {\left(4 - 1\right)}^{2}}$
$= \sqrt{{1}^{2} + {3}^{2}}$
$= \sqrt{1 + 9}$
$= \sqrt{10}$
$= 3.16$
Therefore Circumfernce of the Circle $= 2 \pi r = 2 \pi \times 3.16 \cong 20$
Arc covers $\frac{15 \pi}{8}$ radians on the Circle
In other words Arc covers $\frac{15 \pi}{8} \div 2 \pi = \frac{15}{16} \times$(circumference of the Circle)
Therefore Length of the Arc $= \frac{15}{16} \times 2 \pi r = \frac{15}{16} \times 20 = 18.75$