Let C be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of $ \frac{2\pi}{3}$ at its centre, is :

Question

( A ) $x^2 + y^2 = \frac{9}{4}$
( B ) $x^2 + y^2 = 1$
( C ) $x^2 + y^2 = \frac{27}{4}$
( D ) $x^2 + y^2 = \frac{3}{2}$