# A circle has a center at (7 ,6 ) and passes through (2 ,1 ). What is the length of an arc covering pi  radians on the circle?

length of arc$= 5 \pi \sqrt{2}$

#### Explanation:

compute the radius r first using the two points $\left(7 , 6\right)$ and $\left(2 , 1\right)$

$r = \sqrt{{\left(7 - 2\right)}^{2} + {\left(6 - 1\right)}^{2}} = \sqrt{{5}^{2} + {5}^{2}} = \sqrt{2 \left(25\right)} = 5 \sqrt{2}$

arc $s = r \theta$

$s = \left(5 \sqrt{2}\right) \cdot \pi$

$s = 5 \cdot \pi \cdot \sqrt{2}$

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