A circle's center is at #(3 ,4 )# and it passes through #(3 ,2 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

1 Answer
David G.
Feb 15, 2016

We need to find the radius of the circle and use it to calculate a fraction of the circumference. The distance is #(2pi)/6# #units#.

Explanation:

First find the radius: we know the location of the center and of one point on the edge, so the radius is simply the distance between those points:

#r=sqrt((x_2-x_1)^2+(y_2-y_1)^2) = sqrt((3-3)^2+(2-4)^2)=2# #units#

The circumference of the whole circle, which is #2pi# radians, is #2*pi*r=4pi# units. We want a fraction of that:

#(pi/6)/(2pi)*4pi = (2pi)/6#

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