A circle's center is at #(2 ,4 )# and it passes through #(1 ,2 )#. What is the length of an arc covering #(5pi ) /12 # radians on the circle?

1 Answer
Shwetank Mauria
May 15, 2016

Length of arc is #2.927#

Explanation:

As the center is at #(2,4)# and it passes through #(1,2)#,

the radius is distance between these two points or

#sqrt((1-2)^2+(2-4)^2)-sqrt(1+4)=sqrt5=2.236#

Now, in a circle if #r# is the radius and angle covered by an arc is #theta#, the length of arc is #rtheta# where #theta# is in radians.

Hence, considering #pi=3.1416# and #theta=(5pi)/12#

Length of arc is #(2.236xx5xx3.1416)/12# or #2.927#.

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