A circle's center is at #(9 ,3 )# and it passes through #(2 ,6 )#. What is the length of an arc covering #(2pi ) /3 # radians on the circle?

1 Answer
Somebody N.
Jun 3, 2018

#color(blue)((2pisqrt(58))/3~~15.95043789)#

Explanation:

Arc length is given by:

#rtheta#

Where #theta# is measured in radians.

We first need to find the radius of the given circle. Since the distance from the centre of a circle to any point on its circumference is the radius, we find the distance from:

#(2,6)# to #(9,3)#

Using the distance formula:

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#|r|=sqrt((9-2)^2+(3-6)^2)=sqrt(58)#

Using #rtheta#

#sqrt(58)((2pi)/3)=(2pisqrt(58))/3~~15.95043789#

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