# A circle has a center at (1 ,2 ) and passes through (4 ,2 ). What is the length of an arc covering pi /4  radians on the circle?

Jan 23, 2016

I found $28.3$ units but have a look at my method.

#### Explanation:

I would first find the radius $r$ as the distance between the center and your given point:
$r = \sqrt{{\left({x}_{2} - {x}_{1}\right)}^{2} + {\left({y}_{2} - {y}_{1}\right)}^{2}} = \sqrt{{\left(4 - 1\right)}^{2} + {\left(2 - 2\right)}^{2}} = \sqrt{{3}^{2} + {0}^{2}} = 3$

Then I would consider that the length $s$ of an arc of angle $\theta$ (in radians) will be:
$s = r \cdot \theta$
so that:
$s = 3 \cdot \frac{\pi}{4} = \frac{3}{4} \cdot 3.14 = 28.27 \approx 28.3$ units