A circle's center is at $(5, 2)$ $(5 ,2 )$ and it passes through $(2, 7)$ $(2 ,7 )$ . What is the length of an arc covering $\frac{7 π}{8}$ $(7pi ) /8$ radians on the circle?

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Answer 1 · 2016-04-07T09:04:22

Length of arc $s = 16.0287$ $s=16.0287" "$

Compute the radius $r$ $r$ first

Let Center point $O (x_{o}, y_{o}) = (5, 2)$ $O(x_o, y_o)=(5, 2)$
Let the other point $A (x_{a}, y_{a}) = (2, 7)$ $A(x_a, y_a)=(2, 7)$

$r = \sqrt{{(x_{a} - x_{o})}_{a}^{2} + {(y_{a} - y_{o})}_{a}^{2}}$ $r=sqrt((x_a-x_o)^2+(y_a-y_o)^2)$
$r = \sqrt{34}$ $r=sqrt(34)$

Using the given central angle $θ = \frac{7 π}{8}$ $theta=(7pi)/8$ compute the length of arc

$s = r θ$ $s=rtheta$
$s = \frac{7 \sqrt{34} \cdot π}{8}$ $s=(7sqrt(34)*pi)/8$

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A circle's center is at (5,2)(5 ,2 ) and it passes through (2,7)(2 ,7 ). What is the length of an arc covering 7π8(7pi ) /8 radians on the circle?