A circle's center is at $(3 ,5 )$ and it passes through $(2 ,2 )$ . What is the length of an arc covering $(5pi ) /4$ radians on the circle?

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Answer 1 · 2016-06-15T01:44:31

$12.4unit$

The radius of the circle $R$ is the distance between its center $(3,5)$ to the point $2,2)$ on it.
So $R=sqrt((3-2)^2+(5-2)^2)=sqrt10$

If the length of the arc which subtends angle $5pi/4$ at the center of the circle is S,then

$S/R=5pi/4$

$S=sqrt10xx5/4xx3.14=12.4 unit$

A circle's center is at (3 ,5 )(3 ,5 ) and it passes through (2 ,2 )(2 ,2 ). What is the length of an arc covering (5pi ) /4 (5pi ) /4 radians on the circle?