A circle's center is at #(2 ,4 )# and it passes through #(1 ,2 )#. What is the length of an arc covering #(5pi ) /4 # radians on the circle?

1 Answer
Deepak G.
Aug 19, 2016

Length of the Arc #=8.8#

Explanation:

Circle's center is at #(2,4)# and it passes through #(1,2)#
Therefore Length of the #radius=r# =Distance between these points#(2,4) and (1,2)#
or
#radius =r=sqrt((2-1)^2+(4-2)^2)#

#=sqrt(1^2+2^2)#

#=sqrt(1+4)#

#=sqrt5#

#=2.24#

Therefore Circumference of the Circle #=2pir=2pitimes2.4=14.07#
Arc covers #(5pi)/4# radians on the Circle
In other words Arc covers #(5pi)/4-:2pi=5/8times #(circumference of the Circle)
Therefore Length of the Arc #=5/8 times2pir=5/8 times14.07=8.8#

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