A circle's center is at $(5, 2)$ $(5 ,2 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{7 π}{8}$ $(7pi ) /8$ radians on the circle?

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A circle's center is at $(5, 2)$ $(5 ,2 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{7 π}{8}$ $(7pi ) /8$ radians on the circle?

1 Answer

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Answer 1 · 2016-01-28T04:17:21

$\frac{7 \sqrt{10} π}{8}$ $( 7 sqrt(10) pi ) / 8$

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius $r = \sqrt{{(2 - 5)}^{2} + {(3 - 2)}^{2}} = \sqrt{10}$ $r = sqrt( (2 - 5)^2 + (3 - 2)^2 ) = sqrt(10)$ .
Arc length $S = \frac{7 \sqrt{10} π}{8}$ $S = ( 7 sqrt(10) pi ) / 8$ .

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A circle's center is at $(5, 2)$ $(5 ,2 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{7 π}{8}$ $(7pi ) /8$ radians on the circle?

1 Answer

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1 Answer

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A circle's center is at $(5, 2)$ $(5 ,2 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{7 π}{8}$ $(7pi ) /8$ radians on the circle?