A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(4, 2)$ $(4 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(4, 2)$ $(4 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-02-04T09:18:59

$\frac{π \sqrt{2}}{6}$ $(pisqrt(2))/6$

Explanation:

The circle equation is ${(x - h)}^{2} + {(y - k)}^{2} = r^{2}$ $(x-h)^2 +(y-k)^2 = r^2$ where $(h, k)$ $(h,k)$ is the centre and $r$ $r$ is the radius. We can find $r$ $r$ by substituting in the coordinates of the given point.

${(4 - 3)}^{2} + {(2 - 1)}^{2} = r^{2}$ $(4-3)^2 +(2-1)^2 = r^2$

$1^{2} + 1^{2} = r^{2}$ $1^2 +1^2 = r^2$

$:. r= sqrt(2)$

The complete circle subtends an angle of $2pi (360^o)$ so the arc subtending $pi/6$ represents $(pi/6)/(2pi)$ of the circumference which is $1/12$

Arc length $= 1/12*(2pir) = 2pisqrt(2)/12 =(pisqrt(2))/6$

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A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(4, 2)$ $(4 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

1 Answer

Explanation:

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A circle's center is at (3 ,1 )(3,1)(3 ,1 ) and it passes through (4 ,2 )(4,2)(4 ,2 ). What is the length of an arc covering ( pi ) /6 π6( pi ) /6 radians on the circle?

1 Answer

Explanation:

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A circle's center is at $(3, 1)$ $(3 ,1 )$ and it passes through $(4, 2)$ $(4 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?