A circle's center is at $(2, 1)$ $(2 ,1 )$ and it passes through $(3, 2)$ $(3 ,2 )$ . What is the length of an arc covering $\frac{5 π}{12}$ $(5pi ) /12$ radians on the circle?

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Answer 1 · 2016-03-17T10:19:27

Length of arc covering $\frac{5 π}{12}$ $(5pi)/12$ radian on circle is $1.851$ $1.851$

As the circle's center is at $(2, 1)$ $(2,1)$ and it passes through $(3, 2)$ $(3,2)$ , the distance between these two points will give the radius.

Hence, radius is $\sqrt{{(3 - 2)}^{2} + {(2 - 1)}^{2}} = \sqrt{1^{2} + 1^{2}} = \sqrt{2} = 1.4142$ $sqrt((3-2)^2+(2-1)^2)=sqrt(1^2+1^2)=sqrt2=1.4142$

Hence, length of arc covering $\frac{5 π}{12}$ $(5pi)/12$ radian on circle is

$\frac{5 π}{12} \times 1.4142 = \frac{5 \times 3.1416 \times 1.4142}{12} = 1.851$ $(5pi)/12xx1.4142=(5xx3.1416xx1.4142)/12=1.851$

A circle's center is at (2,1)(2 ,1 ) and it passes through (3,2)(3 ,2 ). What is the length of an arc covering 5π12(5pi ) /12 radians on the circle?