A circle's center is at (2 ,4 ) and it passes through (3 ,1 ). What is the length of an arc covering (13pi ) /8 radians on the circle?

1 Answer
Deepak G.
Aug 16, 2016

Length of the Arc =16.14

Explanation:

Circle's center is at (2,4) and it passes through (3,1)
Therefore Length of the radius=r =Distance between these points(2,4) and (3,1)
or
radius =r=sqrt((3-2)^2+(4-1)^2)
=sqrt(1^2+3^2)
=sqrt(1+9)
=sqrt10
=3.2
Therefore Circumference of the Circle =2pir=2pitimes3.2=19.87
Arc covers (13pi)/8 radians on the Circle
In other words Arc covers (13pi)/8-:2pi=13/16times (circumference of the Circle)
Therefore Length of the Arc =13/16 times2pir=13/16 times19.87=16.14

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