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?

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Answer 1 · 2016-02-06T13:19:57

$4.44$ units

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 $(x-1)^2+(y-3)^2=2$ .

An arc length covering $pi$ radians ( $180^@$ ) is effectively half the circumference of the circle, ie
$1/2xx2pir$

$=1/2xx2xxpixxsqrt2$

$=pisqrt2$ units

$=4.44$ units.

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