A circle's center is at #(2 ,5 )# 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 14, 2016

#=12.4#

Explanation:

Circle's center is at #(2,5)# and it passes through #(1,2)#
Therefore Length of the #radius=r# =Distance between these points#(2,5) and (1,2)#
or
#radius =r=sqrt((2-1)^2+(5-2)^2)#
#=sqrt(1^2+3^2)#
#=sqrt(1+9)#
#=sqrt10#
#=3.16#
Therefore Circumfernce of the Circle #=2pir=2pitimes3.16~=19.87#
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 times19.87~=12.4#

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