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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