A circle's center is at #(4 ,7 )# and it passes through #(9 ,1 )#. What is the length of an arc covering #(5pi ) /3 # radians on the circle?

1 Answer
Deepak G.
Aug 13, 2016

Length of the Arc# ~=41#

Explanation:

Circle's center is at #(4,7)# and it passes through #(9,1)#
Therefore Length of the #radius=r# =Distance between these points#(4,7) and (9,1)#
or
#radius =r=sqrt((9-4)^2+(7-1)^2)#
#=sqrt(5^2+6^2)#
#=sqrt(25+36)#
#=sqrt61#
#=7.81#
Therefore Circumfernce of the Circle #=2pir=2pitimes7.81~=49#
Arc covers #(5pi)/3# radians on the Circle
In other words Arc covers #(5pi)/3-:2pi=5/6times #(circumference of the Circle)
Therefore Length of the Arc #=5/6 times2pir=5/6 times49~=41#

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