If we join the ends of the enterence with center of circle we would get a 45-45-90 triangle with the angle at center = 90 degs

(coz 3/4 th of a circle 3/4*360)

hence sides are in ratio 1:1:sqrt(2)

if r is the radius of the circle, then we have

r*sqrt(2) =12 r =6*sqrt(2)

so perimeter = 3/4 * 2*pi* 6*sqrt(2)

=9pi * sqrt(2)

ans should be C

wow thanks!

didn't realize the two radii formed a 90 degree angle! =)