# A circle's center is at (2 ,7 ) and it passes through (6 ,4 ). What is the length of an arc covering (5pi ) /3  radians on the circle?

May 15, 2018

arc length$= \frac{550}{21}$ units.

#### Explanation:

Let $C \left(2 , 7\right) \mathmr{and} P \left(6 , 4\right)$ be the center and passing point of the circle respectively.

$\rightarrow$Radius of the circle$= C P = \sqrt{{\left(6 - 2\right)}^{2} + {\left(4 - 7\right)}^{2}} = 5 u n i t s$

$\rightarrow \theta = \frac{l}{r}$ where $\theta , l \mathmr{and} r$ are the central angle, arc length and radius of the circle respectively.

$\rightarrow \frac{5 \pi}{3} = \frac{l}{5}$

$\rightarrow l = \frac{25 \pi}{3} = \frac{25 \cdot \frac{22}{7}}{3} = \frac{25 \cdot 22}{7 \cdot 3} = \frac{550}{21} u n i t s$

So, the arc length is $\frac{550}{21}$ units.