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?

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Answer 1 · 2017-11-22T12:11:15

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

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]