A circle's center is at $(9, 3)$ $(9 ,3 )$ and it passes through $(2, 1)$ $(2 ,1 )$ . What is the length of an arc covering $\frac{2 π}{3}$ $(2pi ) /3$ radians on the circle?

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Answer 1 · 2017-11-22T12:11:15

Length of arc covering $\frac{2 π}{3}$ $(2pi)/3$ radians is $15.25$ $15.25$ unit .

Distance between two points $D = \sqrt{{(x_{1} - x_{2})}_{1}^{2} + {(y_{1} - y_{2})}_{1}^{2}}$ $D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2$

Centre $O (9, 3) and P (2, 1)$ $O(9,3) and P(2,1)$ is the point through which

the circle passes. So OP is radius of the circle.

$O P = r = \sqrt{{(9 - 2)}^{2} + {(3 - 1)}^{2}} = \sqrt{53}$ $OP=r= sqrt ((9-2)^2+(3-1)^2) = sqrt 53$

Circumference is $C = 2 \cdot π \cdot r or 2 \cdot π \cdot \sqrt{53}$ $C=2*pi*r or 2*pi*sqrt53$

Arc covering $\frac{2 π}{3}$ $(2pi)/3$ radians is $\frac{1}{3}$ $1/3$ of the circumference

$(2 π)$ $(2pi)$ radians. $:.C/3= (2*pi*sqrt53)/3 ~~ 15.25(2dp)$ unit .

Length of the arc covering $(2pi)/3$ radians is $15.25$ unit .[Ans]

A circle's center is at (9 ,3 )(9,3)(9 ,3 ) and it passes through (2 ,1 )(2,1)(2 ,1 ). What is the length of an arc covering (2pi ) /3 2π3(2pi ) /3 radians on the circle?