A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(5, 2)$ $(5 ,2 )$ . What is the length of an arc covering $\frac{7 π}{12}$ $(7pi ) /12$ radians on the circle?

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A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(5, 2)$ $(5 ,2 )$ . What is the length of an arc covering $\frac{7 π}{12}$ $(7pi ) /12$ radians on the circle?

1 Answer

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Answer 1 · 2016-01-29T05:44:34

$\frac{7 \sqrt{5} π}{12}$ $( 7 sqrt(5) pi ) / 12$

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius $r = \sqrt{{(5 - 3)}^{2} + {(2 - 1)}^{2}} = \sqrt{5}$ $r = sqrt( (5 - 3)^2 + (2 - 1)^2 ) = sqrt(5)$ .
Arc length $S = \frac{7 \sqrt{5} π}{12}$ $S = ( 7 sqrt(5) pi ) / 12$ .

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A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(5, 2)$ $(5 ,2 )$ . What is the length of an arc covering $\frac{7 π}{12}$ $(7pi ) /12$ radians on the circle?

1 Answer

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A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(5, 2)$ $(5 ,2 )$ . What is the length of an arc covering $\frac{7 π}{12}$ $(7pi ) /12$ radians on the circle?