# A circle has a center at (1 ,3 ) and passes through (2 ,4 ). What is the length of an arc covering pi  radians on the circle?

Feb 6, 2016

$4.44$ units

#### Explanation:

The radius of the circle is the distance between the centre and the given point.

r=d((1,3);(2,4))=sqrt((2-1)^2+(4-3)^2)=sqrt2

So the equation of this circle is ${\left(x - 1\right)}^{2} + {\left(y - 3\right)}^{2} = 2$.

An arc length covering $\pi$ radians (${180}^{\circ}$) is effectively half the circumference of the circle, ie
$\frac{1}{2} \times 2 \pi r$

$= \frac{1}{2} \times 2 \times \pi \times \sqrt{2}$

$= \pi \sqrt{2}$ units

$= 4.44$ units.