A circle has a center at $(7, 5)$ $(7 ,5 )$ and passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

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A circle has a center at $(7, 5)$ $(7 ,5 )$ and passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

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Answer 1 · 2016-01-21T19:37:56

$\frac{9 π \cdot \sqrt{5}}{4}$ $(9pi*sqrt(5))/4$

Explanation:

The circle's radius is
$r = \sqrt{{(7 - 1)}^{2} + {(5 - 2)}^{2}} = \sqrt{36 + 9} = \sqrt{45} = 3 \cdot \sqrt{5}$ $r=sqrt((7-1)^2+(5-2)^2)=sqrt(36+9)=sqrt(45)=3*sqrt(5)$

Since the length of an arc covering $2 π$ $2pi$ radians is $2 π \cdot r$ $2pi*r$ , the length of an arc covering $x$ $x$ radians is
$"Arc's Length"=cancel (2pi)r*(x/(cancel(2pi)))=x*r$

In case
$"Arc's Lenght"=(3pi)/4*3*sqrt(5)=(9pi*sqrt(5))/4$

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A circle has a center at $(7, 5)$ $(7 ,5 )$ and passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?

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Explanation:

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A circle has a center at $(7, 5)$ $(7 ,5 )$ and passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{3 π}{4}$ $(3pi ) /4$ radians on the circle?