If it were a complete circle then the missing part of the circle is 1/4 of the circle.

Full circle subtends 360 deg in center.
1/4 of the circle subtends 90 deg in center.

Now draw a triangle with the straight line shown 12 ft as base. Then it will be a isosceles triangle with 90 at origin. It becomes isosceles because the other two sides are radius.

Thus r^2 + r^2 = 12^2

=> 2r^2 = 144

=> r^2 = 72

=> r = 6(2)^1/2

Thus the perimeter of circle = 2 * pie * 6(2)^1/2

Then 3/4th of the circle perimeter = 3/4 * [2 * pie * 6(2)^1/2]

Thus answer = 9 * pie * (2)^1/2

IMO C

shovan85 wrote:If it were a complete circle then the missing part of the circle is 1/4 of the circle.

Full circle subtends 360 deg in center.
1/4 of the circle subtends 90 deg in center.

Now draw a triangle with the straight line shown 12 ft as base. Then it will be a isosceles triangle with 90 at origin. It becomes isosceles because the other two sides are radius.

Thus r^2 + r^2 = 12^2

=> 2r^2 = 144

=> r^2 = 72

=> r = 6(2)^1/2

Thus the perimeter of circle = 2 * pie * 6(2)^1/2

Then 3/4th of the circle perimeter = 3/4 * [2 * pie * 6(2)^1/2]

Thus answer = 9 * pie * (2)^1/2

IMO C

THANKS