A circle's center is at $(1, 2)$ $(1 ,2 )$ and it passes through $(5, 7)$ $(5 ,7 )$ . 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 $(1, 2)$ $(1 ,2 )$ and it passes through $(5, 7)$ $(5 ,7 )$ . 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 · 2016-01-27T03:06:56

$\frac{5 \sqrt{41} π}{3}$ $( 5 sqrt(41) pi ) / 3$

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius $r = \sqrt{{(5 - 1)}^{2} + {(7 - 2)}^{2}} = \sqrt{41}$ $r = sqrt( (5 - 1)^2 + (7 - 2)^2 ) = sqrt(41)$ .
Arc length $L = \frac{5 \sqrt{41} π}{3}$ $L = ( 5 sqrt(41) pi ) / 3$ .

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