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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