A circle's center is at $(5, 4)$ $(5 ,4 )$ and it passes through $(1, 7)$ $(1 ,7 )$ . What is the length of an arc covering $\frac{5 π}{8}$ $(5pi ) /8$ radians on the circle?

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Answer 1 · 2016-11-25T10:10:14

The arc length is $L = \frac{25 π}{8}$ $L=(25pi)/8$

To find the arc length we have to find circle's radius. To calculate it we use the given points. The radius is the distance between given points:

$r = \sqrt{{(5 - 1)}^{2} + {(4 - 7)}^{2}} = \sqrt{4^{2} + {(- 3)}^{2}} = \sqrt{16 + 9} = 5$ $r=sqrt((5-1)^2+(4-7)^2)=sqrt(4^2+(-3)^2)=sqrt(16+9)=5$

Now we can calculate the arc length:

$L = 2 π r \cdot \frac{α}{2 π} = r \cdot α = \frac{5 π}{8} \cdot 5 = \frac{25 π}{8}$ $L=2pir*alpha/(2pi)=r*alpha=(5pi)/8*5=(25pi)/8$

A circle's center is at (5 ,4 )(5,4)(5 ,4 ) and it passes through (1 ,7 )(1,7)(1 ,7 ). What is the length of an arc covering (5pi ) /8 5π8(5pi ) /8 radians on the circle?