The angle #angleCAB# sweeps out some fraction of #o.A#'s full #360^@#, and subsequently the same fractional part of #o.A#'s circumference. To find what the fraction is, we can divide #angleCAB# by #360#:
#(mangleCAB)/360=55/360=11/72#
So, #angleCAB# sweeps out #11/72# of the circle's circumference.
The circumference of any circle is equal to the product of #pi# and the diameter #d# of the circle, which is itself equal to twice the radius, #2r#. Here, we're given #r=AC=12#, so the circle's circumference is #pi*2(12)=24pi#.
So, the length of the arc #BC=11/72*24pi=(24pi*11)/72#
#24# and #72# both have the factor #24# in common, so we can reduce down to
#(11pi)/3#
And we're done.
