Let C be the circle with centre (0,0) and radius 3 units. the equation of locus of the mid-pts of the chords of the circle that subtend and angleof 120 deg at its center is?

Consider chord AC join OA and  OC . Draw perpendicular from O TO B( Mid point of  AC). Let coordinates of B be (h,k). The Angle AOC is 120 deg. Thus angle AOB is 60 deg. Therefore,

   Cos 60= OB/OC. 

   1/2= √h^2 + K^2/3

x^2 + y2 = 9/4