A circle's center is at $(1, 5)$ $(1 ,5 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{π}{4}$ $(pi ) /4$ radians on the circle?

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A circle's center is at $(1, 5)$ $(1 ,5 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{π}{4}$ $(pi ) /4$ radians on the circle?

1 Answer

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Answer 1 · 2016-01-28T04:14:12

$\frac{\sqrt{5} π}{4}$ $( sqrt(5) pi ) / 4$

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius $r = \sqrt{{(2 - 1)}^{2} + {(3 - 5)}^{2}} = \sqrt{5}$ $r = sqrt( (2 - 1)^2 + (3 - 5)^2 ) = sqrt(5)$ .
Arc length $S = \frac{\sqrt{5} π}{4}$ $S = ( sqrt(5) pi ) / 4$ .

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A circle's center is at $(1, 5)$ $(1 ,5 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{π}{4}$ $(pi ) /4$ radians on the circle?

1 Answer

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A circle's center is at $(1, 5)$ $(1 ,5 )$ and it passes through $(2, 3)$ $(2 ,3 )$ . What is the length of an arc covering $\frac{π}{4}$ $(pi ) /4$ radians on the circle?