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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