A circle's center is at #(3 ,1 )# and it passes through #(6 ,6 )#. What is the length of an arc covering #(13pi ) /12 # radians on the circle?

1 Answer
Alan P.
Feb 17, 2016

#19.845#

Explanation:

The radius of the circle is
#color(white)("XXX")r=sqrt((6-3)^2+(6-1)^2) = sqrt(3^2+5^2) = sqrt(34)#

Since a circle has a circumference (arc length) of #2rpi#
and an arc angle of #2pi#:
#("arc length")/("arc angle") = (2rpi)/(2pi) = ("required arc length")/((13pi)/12)#

#"required arc length"=(13pi)/12*(cancel(2)rcancel(pi))/(cancel(2)(cancelpi))=(13pir)/12#

#color(white)("XXXXXXXXXXX")=(13sqrt(34)pi)/12#

#color(white)("XXXXXXXXXXX")~~19.845# (using a calculator)

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