A circle's center is at $(3, 4)$ $(3 ,4 )$ and it passes through $(0, 2)$ $(0 ,2 )$ . 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 $(3, 4)$ $(3 ,4 )$ and it passes through $(0, 2)$ $(0 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-01-22T23:20:35

Center of circle is at $(3, 4)$ $(3,4)$ , Circle passes through $(0, 2)$ $(0,2)$
Angle made by arc on the circle= $\frac{π}{6}$ $pi/6$ , Length of arc $= ? ?$ $=??$

Let $C = (3, 4)$ $C=(3,4)$ , $P = (0, 2)$ $P=(0,2)$

Calculating distance between $C$ $C$ and $P$ $P$ will giveus the radius of the circle.

$| C P | = \sqrt{{(0 - 3)}^{2} + {(2 - 4)}^{2}} = \sqrt{9 + 4} = \sqrt{13}$ $|CP|=sqrt((0-3)^2+(2-4)^2)=sqrt(9+4)=sqrt13$

Let the radius be denoted by $r$ $r$ , the angle subtended by the arc at the center be denoted by $θ$ $theta$ and the length of the arc be denoted by $s$ $s$ .

Then $r = \sqrt{13}$ $r=sqrt13$ and $θ = \frac{π}{6}$ $theta=pi/6$

We know that:
$s = r θ$ $s=rtheta$

$\Rightarrow s = \sqrt{13} \cdot \frac{π}{6} = \frac{3.605}{6} \cdot π = 0.6008 π$ $implies s=sqrt13*pi/6=3.605/6*pi=0.6008pi$

$\Rightarrow s = 0.6008 π$ $implies s=0.6008pi$

Hence, the length of arc is $0.6008 π$ $0.6008pi$ .

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A circle's center is at $(3, 4)$ $(3 ,4 )$ and it passes through $(0, 2)$ $(0 ,2 )$ . What is the length of an arc covering $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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