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

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A circle has a center at $(1, 2)$ $(1 ,2 )$ and passes through $(4, 3)$ $(4 ,3 )$ . 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 · 2016-01-28T04:33:34

$\frac{\sqrt{10} π}{4}$ $( sqrt(10) pi ) / 4$

Explanation:

Please check my solution here for a detailed explanation.

Solution
Radius $r = \sqrt{{(4 - 1)}^{2} + {(3 - 2)}^{2}} = \sqrt{10}$ $r = sqrt( (4 - 1)^2 + (3 - 2)^2 ) = sqrt(10)$ .
Arc length $S = \frac{\sqrt{10} π}{4}$ $S = ( sqrt(10) pi ) / 4$ .

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

1 Answer

Explanation:

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