Question

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

Answer 1

Length of arc covering `(2pi)/3` radians is `15.25` unit .

Explanation:

Distance between two points `D= sqrt ((x_1-x_2)^2+(y_1-y_2)^2`

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

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

`OP=r= sqrt ((9-2)^2+(3-1)^2) = sqrt 53`

Circumference is `C=2*pi*r or 2*pi*sqrt53`

Arc covering `(2pi)/3` radians is `1/3` of the circumference

`(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]