A circle's center is at $(3 ,9 )$ and it passes through $(4 ,5 )$ . What is the length of an arc covering $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-02-08T22:15:28

Arc Length: $s=R.\theta=\frac{\pi}{6}.\sqrt(17)$ units

The distance between points ( $x_0, y_0$ ) and ( $x,y$ ) is :
$\sqrt((x-x_0)^2+(y-y_0)^2)$

Radius is the distance between the centre ( $x_0, y_0$ ) and a point on the circle ( $x,y$ ).

Radius: $R=\sqrt((4-3)^2+(5-9)^2)=\sqrt(17)$ units,
Arc Length: $s=R.\theta=\frac{\pi}{6}.\sqrt(17)$ units

A circle's center is at (3 ,9 )(3 ,9 ) and it passes through (4 ,5 )(4 ,5 ). What is the length of an arc covering ( pi ) /6 ( pi ) /6 radians on the circle?