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

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

1 Answer

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Answer 1 · 2016-01-28T04:34:49

$\frac{5 \sqrt{13} π}{3}$ $( 5 sqrt(13) pi ) / 3$

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius $r = \sqrt{{(5 - 7)}^{2} + {(8 - 5)}^{2}} = \sqrt{13}$ $r = sqrt( (5 - 7)^2 + (8 - 5)^2 ) = sqrt(13)$ .
Arc length $S = \frac{5 \sqrt{13} π}{3}$ $S = ( 5 sqrt(13) pi ) / 3$ .

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

1 Answer

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