A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{5 π}{12}$ $(5pi ) /12$ radians on the circle?

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{5 π}{12}$ $(5pi ) /12$ radians on the circle?

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Answer 1 · 2016-05-15T10:51:47

Length of arc is $2.927$ $2.927$

Explanation:

As the center is at $(2, 4)$ $(2,4)$ and it passes through $(1, 2)$ $(1,2)$ ,

the radius is distance between these two points or

$\sqrt{{(1 - 2)}^{2} + {(2 - 4)}^{2}} - \sqrt{1 + 4} = \sqrt{5} = 2.236$ $sqrt((1-2)^2+(2-4)^2)-sqrt(1+4)=sqrt5=2.236$

Now, in a circle if $r$ $r$ is the radius and angle covered by an arc is $θ$ $theta$ , the length of arc is $r θ$ $rtheta$ where $θ$ $theta$ is in radians.

Hence, considering $π = 3.1416$ $pi=3.1416$ and $θ = \frac{5 π}{12}$ $theta=(5pi)/12$

Length of arc is $\frac{2.236 \times 5 \times 3.1416}{12}$ $(2.236xx5xx3.1416)/12$ or $2.927$ $2.927$ .

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{5 π}{12}$ $(5pi ) /12$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at (2,4)(2 ,4 ) and it passes through (1,2)(1 ,2 ). What is the length of an arc covering 5π12(5pi ) /12 radians on the circle?

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A circle's center is at $(2, 4)$ $(2 ,4 )$ and it passes through $(1, 2)$ $(1 ,2 )$ . What is the length of an arc covering $\frac{5 π}{12}$ $(5pi ) /12$ radians on the circle?