A circle's center is at $(7, 2)$ $(7 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?

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A circle's center is at $(7, 2)$ $(7 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?

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Answer 1 · 2016-08-07T14:19:31

$= 34.76$ $=34.76$

Explanation:

So the distance between points $(7, 2)$ $(7,2)$ and $(5, 8)$ $(5,8)$ is the radius of the circle.
So the distance is
$= \sqrt{{(7 - 5)}^{2} + {(8 - 2)}^{2}}$ $=sqrt((7-5)^2+(8-2)^2$
$= \sqrt{2^{2} + 6^{2}}$ $=sqrt(2^2+6^2)$
$= \sqrt{4 + 36}$ $=sqrt(4+36)$
$= \sqrt{40}$ $=sqrt40$
$= 6.32$ $=6.32$
Therefore radius of the Circle $r = 6.32$ $r=6.32$
The Circumference of the circle $= 2 π r = 2 π (6.32) = 39.73$ $=2pir=2pi(6.32)=39.73$
An Arc covers $7 \frac{π}{4}$ $7pi/4$ radians
or
It covers $7 \frac{π}{4} \div 2 π = \frac{7}{8}$ $7pi/4-:2pi=7/8$ of the Circumference
Therefore; Length of the Arc $= \frac{7}{8} (39.73) = 34.76$ $=7/8(39.73)=34.76$

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A circle's center is at $(7, 2)$ $(7 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at $(7, 2)$ $(7 ,2 )$ and it passes through $(5, 8)$ $(5 ,8 )$ . What is the length of an arc covering $\frac{7 π}{4}$ $(7pi ) /4$ radians on the circle?